Linking Group Theory to Social Science Game Theory: Interaction Grammars, Group Subcultures and Games for Comparative Analysis

Abstract

This article draws on earlier work in social system theorizing and analysis—in particular, the theory of social rule systems. On the basis of this foundational work, its aim is to systematically link theories of social groups and organizations, on the one hand, and social science game and interaction theory, on the other hand. Rule system theory has contributed to significant features of group theory and social science game theory. It is a cultural-institutional approach to conceptualizing group systems and games. We explore how groups and their particular games can be effectively described, analyzed, and compared—and their similarities and differences identified on a systematic basis. For illustrative purposes, we present a selection of several ideal types of groups: a military unit, a terrorist group, a recreational or social group, a research group, and a business entity, each of whom has a distinct rule configuration making for particular “rules of the game” and game patterns of interaction and outcome.

1. Group Theory, Game Theory, and Their Interlinkage: An Overview

1.1. Introduction

Group theory derives from the theory of social rules and rule complexes applied to describing, analyzing, and explaining diverse types of groups and organizations and their particular patterns of behavior. The theory conceptualizes group interaction grammars as rule regimes that structure and regulate social relationships and interaction patterns in any given group or organization: (1) It states that the grammars are complexes of rules applying to institutionalized relationships and interactions of individuals, groups, and organizations; (2) The research conceptualizes and applies rules and rule complexes and their derivatives with respect to roles, role relationships, norms, group procedures and production functions and their performances; (3) it identifies a finite and universal set of rule categories (10) making up a rule regime (a major subsystem of any functioning group, organization, or community); (4) the theory conceptualizes particular “group rule configurations”—rule regimes for any given group with specified, more or less compatible rules in the universal rule categories; (5) groups are identifiable as well as differentiable by their particular rule configurations (as well as by their resource and agency bases). The article emphasizes the differentiating character of any given group’s distinct rule configuration or sub-culture—the actual complex of rules guiding and regulating behavior in any given group. Groups are distinguishable (and comparable) in terms of the content of their finite rule categories: rules concerning group identity, purposes, social relations, production algorithms, internal and external governance, time and place rules. Groups may change rules in their configuration in response to external and/or internal changes, pressures, incentives, performance failings.

Social science game theory (SGT) is based on the formulation of a theory of rules and rule systems with a systematic grounding in contemporary social sciences. Sociological concepts such as norm, value, belief, role, social relationship, and institution can be defined in a uniform way in SGT in terms of rules, complexes of rules, and rule regimes. Group rule configurations provide a conceptual linkage between group theory and game theory. They are the core of “rules of the game” and the rule-based patterning of interactions and outcomes for different types of groups. The theory is applied to games such as classical games (e.g., cooperative and non-cooperative games, PD games, zero-sum games, etc.) At the same time, the theory is applicable to non-strategic situations, in particular routine, institutionalized interactions (many role interactions are of this sort), rituals, ceremonies—with little or no significant decisions or choice activities.

1.2. Rule Regimes, Group Properties (Relations/Structures), and Group Differentiation

In this section, the theory of social rules and rule regimes is applied to group theory for describing, analyzing, and explaining diverse types of groups. (As indicated above, the same theory is also used in the formulation of a social science game theory.1) Rule system theory provides a model which identifies key specific rule categories which underlie or, when enacted, generate particular group or organizational properties and patterns: the rules concern a group’s particular participants and their relations and social structure, its times and places, its values and goals, its activities and procedures and productions, its materials and technologies used in group activities and production functions. They concern the finite and universal rule base of group social action and interaction, its material, social structural, and agential conditions.

The rule regime conceptualization is a basis to describe, differentiate, and explain groups (consisting of collective identity membership, social structure, particular patterns of activities, and outputs (products, types of performance, developments)).

1.2.1. Rule Regimes and Social Relations/Structures

Most human social activity—in all of its extraordinary variety—is organized and regulated by socially produced and reproduced rules and systems of rules (Burns and Flam 1987; Giddens 1984; Harre 1979).2 Such rules are not transcendental abstractions. Rule regimes are carried, applied, adapted, and transformed by concrete human agents (individuals, groups, and communities)—in their language, customs and codes of conduct, norms, and laws and in the social institutions of the modern world, including family, community, market, business enterprises and government agencies. The agents interact, exchange, struggle, and exercise power in their particular group and organizational contexts, in large part based on the rule regimes regulating them and which they maintain, adapt, and transform.

The making, interpretation, and implementation of social rules are universal in human societies, as are their reformulation and transformation. Human agents (individuals, groups, organizations, communities, and other collectivities) produce, carry, and reform these systems of social rules, but this frequently takes place in ways they neither intend nor expect.3

On the macro-level of culture and institutional arrangements, we speak of established rule system complexes or rule regimes such as the language, cultural codes and forms, shared paradigms, norms and “rules of the game”.4 On the actor level these translate into roles, particular norms, strategies, action paradigms, and social grammars (for example, procedures of order, turn-taking and voting in committees and democratic bodies).5 Social grammars of action are associated with culturally defined institutional domains and roles, indicating particular ways of thinking, judging, and acting. For instance, in the case of gift giving or reciprocity in defined social relationships, actors display their social and cultural competence in knowing when and to whom a gift should be given or not, how much it should be worth, or, if one should fail to give it or if it lies under the appropriate value, what excuses, defenses and justifications might be acceptable. Rules and rule systems serve three (at least) basic functions/uses in all social life: (1) coordination/direction of social action and interaction; (2) understanding/simulation of what is going on or will go on in the future; and (3) referents in giving and asking for accounts, generating normative discourses, for instance of praise and of critique.6

The rules making up rules regimes consists of three qualitatively different kinds of rules: descriptive or declarative rules describing or defining reality, action or directive/regulative rules, and evaluative rules defining what is worth-while, good, valuable (or their opposites, “bads”).

One of the contributions of rule system theory has been in conceptualizing universal interaction grammars (Burns and Flam 1987). Such grammars are complexes of rules applying to social action and interaction of individuals, groups, and organizations. These grammars consist of a finite set of rule types or categories that are identified in the following section.7

1.2.2. Universal Interaction Grammars8

We have identified and applied universal rule grammars—in a comparative perspective—to human interaction and games as well as diverse institutions and institutional arrangements: bureaucracies, judicial systems, markets, democratic associations, etc.9

The conceptualization of universal interaction grammars enables us to systematically investigate and analyze group and organizational structures, interaction situations and performances, which rule regimes socially defined and regulated—and to do this comparatively—as one would compare the grammars of different languages. This is done in Burns and Flam (1987) in terms of defining social relationships and interaction patterns of diverse institutions.10

In the model of group and organizational rule regimes, ten (10) categories of rules are identified (see

Table 1. Key Types of Rule Categories Specifying Group Conditions, Structures, and Processes.12

Rule Types	Definitions
Type I	Identity rules—“Who are we?” “What symbolizes or defines us?”
Type II	Membership, Involvement, and Recruitment Rules—“Who belongs, who doesn’t?” “What characterizes members?” “How are they recruited?”
Type III	Rules concerning shared value orientations and ideals—“What does the group consider good and bad?”
Type IV	Rules concerning shared beliefs and models—“What do we know and believe about ourselves, our group behavior, and our environment”.
Type V	Social relational, group structuring, and governance rules. “How do we relate to one another, what is our social structure?” “What are the authority and status differences characterizing the group?” “How do we interact and reciprocate with one another and with the leadership?” “What are the rules of internal governance and regulation?”
Type VI	Rules for dealing with environmental factors and agents (“external governance”). “How do we cope with, make gains in the environment, dominate, or avoid environment threats?”
Type VII	Group production and activity rules. “What are our characteristic activities, practices, production programs, ceremonies and rituals?” “How do we coordinate activities and make collective decisions?”
Type VIII	Rules and procedures for changing the rule regime, or for changing core group conditions and mechanisms. “How do we (or should we) go about changing group structures and processes, our goals, or our practices?”
Type IX	Technology and resource rules. “What are appropriate technologies and materials we should use in our activities (and possibly those that are excluded)?”
Type X	Time and Place Rules—“What are our appropriate places and times?”

,

Table 2. Illustration of a Particular Group Rule Configuration.

Rule Type	Terrorist Group Rule Configuration (For instance, the 9/11 Group; see Dermott 2005; Kean 2014; also Table 3)
Defining Identity (I)	Group name, possibly logo. Identity associated with the terrorist goals and possibly with the particular methods or strategies used. “Negative” dress code to conceal identity when operating clandestinely.
Recruitment of Membership Participation/Involvement (II)	Recruitment and training of capable and committed members, willing and able to carry out terror acts. Covert participation. Dress code and code of silence to conceal identity. Strict obedience to leaders and group rules.
Shared Value(s), Purposes, Goals (III)32	Orientation to carry out deadly attacks against designated categories of targets; accomplish destabilizing actions, create terror.
Shared beliefs/Model of reality rules (IV)	The world is divided between Muslim believers and non-Muslim believers; the latter are enemies, polluters that will undermine and destroy Islam. Even some “quasi” Muslim groups are a threat to a holy Islam.
Group Relations of Reciprocity and Leadership (V)	Strict hierarchy, maintenance of strict separation among members (thus, independent cells).
Production and Output Functions (group protection and maintenance; hostile and destructive actions) (VI)	Deployment and use of terrorist weapons; actions to conceal identity and operations. Procurement of weapons, safe houses, financing; Appealing to potential recruits.
Relations with the Environment (VII)	Identification of enemies and targets; concealment, avoiding detection and monitoring. Identification of potential recruits.
Rules and Procedures for Changing the Rule Regime, Particular Rules	Ways the group changes rules, roles, and policies. Typically, part of an authoritative hierarchy.
Group Resources (IX) (materials and technologies)	Weapons of destruction; safe houses. Sufficient funding to obtain weapons and establish effective concealment; and to engage in the preparations such as training and travel.
Times and Places for Group Activities (X)	24-7 readiness, available safe group spaces, training camps.

and

Table 3. Illustrations of Group Rule Configurations.

	Business Unit (A) (Illustration)	R&D Institute (B) (Illustration)	Recreational, e.g., a Club (C) (Illustration)	Professional Army Unit (D) (Illustration)	Terrorist Group (Illustration) (E)	Prison Institution (F) (Illustration)
Defining Identity (I)	Trade name, logo; possibly badges, dress code, even uniforms. Likely a particular location or building(s). Identity also defined by the goal orientation to economic gain (which often trumps other goals) (see category III)	Institute name, possibly logo. Minimal or no dress code. Identity associated with the research goals, typically in a particular research area and possibly with the methods or equipment used.	Group name (e.g., club name), possibly with logo. Minimal or no dress code. Identity associated in part with the particular group activity and its location.	Unit's name, logo or insignia and markings of rank. Particular military uniform as dress code. Possibly a particular location. Identity in part defined by the goal orientation and the means used (military power) (see rule categories (III) and (VI))	Group name, possibly logo. Identity associated with the terrorist ideology and goals and possibly with the particular methods or strategies used. “Negative” dress code to conceal identity	Prison name. Guards also uniformed. Identity associated with the purposes, means, technologies, characteristics of the prison and its population. Prisoners typically subject to a uniform dress code. Thus, dual social order
Recruitment (II)	Skill-based recruitment; Search for persons and groups sufficiently oriented to and acceptant of remuneration levels provided as well as performance demands	Recruitment based on expertise/merit, and/or formal education/training of individuals or groups in the relevant field or domain of the group.	Affinity group of friends, relatives or people with common interest in the recreation (“buffs”) and getting together.	Formal recruitment and training of able and willing unit members to obey and perform violent acts (based on honor, payment (mercenaries), conscription (coerced involvement))	Recruitment and training of capable and committed members, willing and able to carry out terror acts	Guards are recruited. Strictly speaking, prisoners are not “recruited”. They have been arrested and confined. Thus, again a dual social order.
Membership and Participation/Involvement (II)	Contractual engagement. Members are remunerated and with careers and rewards for high performance. Sanctioning for disloyalty and disobedience.	Members are remunerated and with careers. Informal, relatively lax sanctioning for breaking group norms and values. Loyalty to the knowledge production cause and the professional code of ethics—negative sanctioning for deviance from these.	Informal, relatively lax sanctioning for breaking group norms and values. However, there are limits.	Members are typically remunerated and with careers in modern armies. Highly codified, harsh punishment for breaking key group rules, in particular those concerning loyalty and obedience to the leadership, group norms, and its symbols	Covert participation. Dress code and code of silence to conceal identity. Strict obedience and loyalty to leaders, group rules, and symbols.	Dual social order. Guards are remunerated and with careers—and are expected to obey rules and exhibit loyalty to the prison administration. Prisoners are alienated and generally oppositional.
Purposes/Values (III)39	Pursuit of money-making; possibly also values of making quality goods and services, satisfying clients	Produce new knowledge or technology. Innovate/create and experience “flow”, possibly also to achieve symbolic power and scientific prestige as well as “gains in resources”.	Mutual pleasure, getting together, “having fun”	Defense/ Offense (external); also, orientation to possibly exercising control internal to the society (coups)	Orientation to carry out deadly or intimidating attacks against designated categories of targets; create terror, accomplish destabilizing actions.	Maintain law and order. Divided (and divisive purposes) between guards and prisoners.
Group Relations of Governance, Leadership and Reciprocity (V)	Hierarchical social order. Supervisor planning and monitoring of production activities; regulating and sanctioning inappropriate deviance	Professional forms of governance and regulation. Likely status differences and symbolic hierarchical order. Exchange, reciprocity, and competition more generally.	Minimal formality and hierarchy but possibly with status differences. Usually amicable negotiations and agreements among members. Someone or some members expected to plan and coordinate meetings	Strict hierarchy and stringent monitoring and sanctioning of behavor. Possibly high reciprocity and support among members	Strict hierarchy, maintenance of sharp separation among units (individuals and subgroups)	Prison leadership and guards make up an administrative system. Prisoners form informal groups for recreation, illegal activity
Production Functions and Outputs (VI)	Gaining necessary materials and technologies. Performing production and commercial activities. Achievement of economic gain from production and commercial activities	Gaining necessary materials and technologies. Performing research. Initiate and accomplish potentially innovative or creative projects along with publishing and gaining scientific recognition and status.	Gaining access to activity space, materials, and technologies for group activities. For instance, engagement in particular sport activities (amateur)	Gaining access to territory, technologies, and other materials as well as financing. Deployment and exercise of armed force or its threat, for instance in territorial defense or offensive action.	Procurement of weapons, funding, and access to safe houses. Deployment and use of terrorist weapons; action to conceal identity and operations.	Prison administration has prison routines and technologies (including weapons) to control prisoners. Prisoners typically try to engage in various illegal or forbidden activities
Relations with the Environment (VII)	Rules and strategies for dealing with financers, suppliers, competitors, and regulators Oriented dynamically to goods and services markets.	Rules and strategies for dealing with funders, suppliers, competitors, regulators, and the professional community. Strategies vis-à-vis funders, competitors, relevant professional communities	Loose boundaries. But rules and strategies for dealing with suppliers and regulators as well as others in the environment	Strategies for obtaining essential materials, technologies and financing. Dealing with funders, suppliers, and regulators Dealing with external enemies or threats. Maintaining strict boundaries.	Dealing with funders and suppliers as well as with monitors and potential observers. Identification of enemies and targets as well as threats; concealment, avoiding detection and monitoring	Prison administration deals with funders, suppliers, and regulators Prison tries to strictly control prisoner exchanges with the environment.
Rules and Procedures for making or Changing Rules (VIII)	Dual system. Group management or higher management engages in meta-powering and rule changing	Flexible, individual choice, or possible collective choice, either through multi-actor negotiation or voting	Flexible, Easygoing	Dual system. Authoritative—either group leaders or higher levels make or change rules.	Dual system. Authoritative—either group leaders or superior levels but highly clandestine	Dual system. Prison administration makes and changes rules (also, from external law and policy-making). Prisoners have their own ways for making and changing rules, but typically clandestine
Group Resources (IX) (materials and technologies).	Specified appropriate materials, technologies used in production and commercial activities; Sufficient financial resources (capital) for group sustainability and production.	Appropriate resources and equipment for research and development in the group’s domain (e.g., computers, special equipment, programs, laboratories). Sufficient funding base is a critical component of group knowledge production and sustainability.	Specified equipment for activities; access to activity space	Armaments, military equipment, access to territory to locate in. Sufficient funding to function effectively relative to real or potential military challenges	Weapons of destruction; safe houses. Sufficient funding to obtain weapons and to engage in preparations such as training and maintaining save houses and weaponry.	Prison administration has substantial resources of control and sanctioning. Prisoners have to smuggle in or to produce themselves many of their technologies and other materials
Times and Places for Group Activities (X)	Specified times and places (factory, office) for production, bur possibly with “farming out” and Flextime—thus likely fuzziness and variability.	Flexible or loose times and places for research (work).	Free time of members; identity of places accessible to members or the group as a corporate entity (club).	24-7 readiness, military camps and offensive and defensive positions. Specified territory or territories for bases.	24-7 readiness. Available safe group spaces, training camps	Administration has 24-7 readiness. Prisoner times and places decided by prison administration and/or courts

Notes: (1) This table concerns rule complexes which, when enacted, generate patterns of group interaction and outcomes/outputs. There is substantial variation in patterns among diverse groups. Such variation is traceable to differences in group rule configurations and in their situational contexts; (2) Note that groups A, B, D, E and F involve task-oriented groups (there are goals, means, specific membership recruitment, governance structures, conceptions and “measures” of success and failure, and reflectivity and, under some conditions, predisposition to reform (see Category VIII)). C, on the other hand, is expressive or “fun” oriented; group activity itself and the experience of pleasure are the aims. However, to engage in a fun activity such as to bowl or to play basketball together, the group has to make arrangements and gain access to, for example, a bowling alley or a basketball court—and dealing with the rules and demands of these facilities becomes a preoccupation or goal consideration (group requisites and derivative goals). Group E (and possibly A, B, and D as well) are task as well as expressive oriented in that there is high emotional involvement of members in productive activities and group matters; (3) A group may undergo changes as a result, for instance, of the development of new goals, new technologies, or new production complexes. Thus, a recreational group might develop a more professional and ultimately business-like orientation with concerns about improved performance, competitivity and obtaining money to finance better technology and qualified participants. Or, an informal research group or network may institutionalize itself within a university, or may establish an independent institute on its own but with appropriate goals about obtaining sustained funding, a physical location and edifice—and, of course, satisfying external requirements for the appropriate features of its organization, membership, and productive activities. Note that time rules in business and research groups have been changing, for instance, more flexible times for group activities (Flextime). Also, space rules are changing with many businesses and research groups as well as military units are globalizing (changing territories and space conditions and rules). Technological systems such as the internet are obviously playing a major role here; (4) For military, prison, and terrorist groups, governance entails hierarchical systems with strict rules of command and obedience. In other words, the rules tend to be stringently applied, monitoring is systematic, and there is considerable disciplinary sanctioning—even substantial internal physical and psychological violence. In research and social play groups, there is more likely to be rules of collegiality and negotiation for internal governance and the changing or reform of group rules. Business governance operates with hierarchy as well as negotiation forms; physical and even psychological violence tends to be low in many such contexts; (5) Rules concerning the requirements of recruits and participants varies a great deal: To a greater or lesser extent, loyalty to the group and its norms and arrangements is typical of any group. But some groups require high loyalty: for instance, the military and terrorist groups. Merit and skill are important for military, business, and science groups as well as terrorist groups such as Al-Qaeda.

) concerning group agency conditions, social structure, interaction, material conditions, and time and space: (A) Four categories concern agency relating to: Identity (I), Group membership (II), Share values, ideals, and goals (III), and Shared knowledge and beliefs (IV); (B) Group social relations and structure (category V); (C) Group action and interaction orders/patterning (VI, VII, VIII); (D) Material and resource conditions of group action and interaction (IX); and (E) Rules relating to group times and space conditions for group meetings and interactions.11

This regime is the basis of a cognitive-normative framework defining among other things group identity, its purposes, structural architecture, role relations including status and authority relations, groups divisions, procedures, characteristic activities, and patterns of interaction and production/outputs.13 The regime may be understood as consisting of a collective codebook, cultural tools and social organizational principles. There is an architecture of any rule regime, the cognitive-normative basis of the formation and functioning any group or organization (see Appendix A for illustrations).

Rules that are part of a group’s rule regime are to a greater or lesser extent “known” to group members (some or many tacitly known); they are normally useable/implementable or applicable (provided requisite technologies and resources are available to the actor(s); and are considered functional or appropriate (or legitimate, as rules in an established regime). A group’s regime provides the cognitive-normative basis of members to coordinate with one another, to collaborate and exchange in particular ways; to understand what is going on in the group, to simulate groups interactions and developments, and to refer to in giving and asking for accounts and in making normative judgments, criticisms as well as eulogies.

The theory does not require that the participants in interaction are in agreement with the rule regime (or any of its sub complexes). Group actors in diverse roles are expected to perform according to different grammars, but they may disagree and struggle over the appropriate grammars, the contents of particular categories of rules, or even details of a particular rule. As stressed in Burns and Flam (1987) (also see Burns and Hall 2012), there is at one time or another a “politics” (or potential politics) to social rules, those rules that are supposed to apply generally as well as the rules associated with particular roles, role relationships, production functions, and governance activities.

The ten universal rule categories presented here may not be fully specified in all interaction situations. Typically, the process of “institutionalizing” a group or a complex of relationships may entail overtime a piecemeal specification of the rules in the different categories. Long established—institutionalized—groups and their relationships usually have rules specified in all the categories. However, this is an empirical question.14 Also, disruptions may occur as a result of political, economic, technological, or other social changes. Rules in particular categories that were taken for granted earlier may no longer be accepted or applied. Relationships which were hierarchical (with rule specifications appropriate to such relationships) are transformed into egalitarian relationships. Or the values and norms considered appropriate for particular relationships (whether in a family, religious community, work organization, political association) are transformed, shift, or are prioritized in radically different ways.15

1.3. Social Science Game Theory in a Nutshell (SGT)16

In SGT games consist of (1) participating, mutually aware agents whose actions are interdependent; (2) rule regimes (cultural and institutional conditions and forms); and (3) resources (technologies, material conditions). Most games are embedded in rule systems making up social institutions and cultural foundations (Burns and Flam 1987).

(1) SGT theory is developed and applied to multi-agent interaction situations where there are interdependencies among two or more of the agents (as in classical game theory).

(2) A SGT game consists of a set of actors whose actions and action outcomes are interdependent; they interact in complex social and psychological contexts, subject to particular rule regimes (institutions, cultural formations (see Figure 1)) as well as material and technological constraints. Games are socially embedded—normative, relational, and institutional contexts are identified and taken into account in their influence on interaction conditions and perceptions, judgments, and actions of the participating actors.

Interaction and group behavior, its outputs (and consequences) are patterned in large part through actors performing their roles and adhering to norms; at the same time, they may make strategic choices, take strategic actions to better achieve a goal or to realize a role or norm (games are open).

(3) SGT provides a cultural/institutional basis for the conceptualization and analysis of games in their social context, showing precisely the ways in which social norms and rule complexes of social relationships, values, institutions, and social relationships come into play in shaping and regulating game agents and their interactions.

(4) The SGT approach to game theorizing rejects assumptions of super-rationality and maximization of one-dimensional utility. Instead, it stresses human choice and action based on social rule systems—in many of not most instances implementing norms, roles, and institutional arrangements.17 Typically, some or many properties of interactions and outcomes are unknown (unanticipated and unintended outcomes of actions and interactions are an inherent part of the SGT conceptualization).

(5) SGT distinguishes between open and closed games. The rule regime or structure of a closed game is fixed. In open games, actors have the capacity to structure, restructure, and transform game components such as the role components or the general “rules of the game”. Even external agents (“third parties”) may have the power (“meta-power”) to structure and transform games (hence, “the prisoners’ dilemma game has been analysed in SGT as a three-person game”).18 Each player has one or more roles in the game; in her role an actor has a set of given strategies in closed games; in open games, she may develop strategies as the interactions among players evolve. In general, actors may to a greater or lesser extent change the strategies or option as well as the rules, roles, norms, players, context, etc.

(6) Rules governing Communicative actions. Communication conditions and forms are specified by the rules defining action opportunities and repertoires in any given game situation.

In whatever ways the norms and institutional arrangements are established and maintained, the sociological approaches provide a language and analytic tools to describe and analyze a wide variety of communication situations distinguishable by their particular group norms and institutional arrangements.19

(7) Extraordinary Social Knowledge. While SGT readily and systematically incorporates the principle that human actors have bounded factual knowledge and computational capability, it emphasizes their extraordinary socio-cultural and institutional knowledge and competences: in particular, their knowledge of diverse cultural forms and institutions such as in the context of family, market, government, business or work organization, hospitals, and educational systems, among others, knowledge which they bring to bear in framing and engaging in their social relationships and game interactions.

(8) Action Determination Array. The action determination array (DET[G,S, i]) consists of a finite set of algorithms for determining action (including response(s) in relation to the actions of others). Each modality has one or more algorithms that generate actions or make selections of action, for instance, algorithms for implementing or “following” a ritual, norm, role, role relation (together with others), or an institutional arrangement; judgment algorithms for choosing or shaping action alternative(s).20

The concept of action determination refers to the basis on which actors perform and action, make choices among given alternative actions, or construct their actions. Games in the SGT perspective range from rule prescribed social actions and interactions to actions and interactions that entail various degree of choice. Three main classes of ideal-type algorithms of action determination are distinguished: algorithms for implementing a rule or rule complex, algorithms or procedures for choosing among alternatives, and algorithms and strategies for constructing or creating an action.

A. DET-I: Following or implementing an appropriate or prescribed norm, role, institutional arrangement (with multiple participants), that is a rule complex or algorithm is implemented. Social actions and interactions are routinized, ritualistic; performance or enactment is matched with a specified norm or procedure in a given interaction situation S and game G, with actors i,j,k... in their role and role relationships. If two actors, A and B, in a 2-person game have established paired rule complexes to implement, the interaction is routine/predictable. Even if content changes—within some limits—the interaction is produced in routine and predictable ways.

The procedures for following or implementing a rule or rule complex: There is activation of the rule or rule complex and the performer compares and “matches” the experience or perception of the act with the qualities or details specified by the rule or rule complex. (Whole production systems operate more or less in this way: organ transplantation systems (Machado 1998); hydro-power planning and decision-making frameworks (Burns and Flam 1987)).

B. DET-II: This type of algorithm applies to assessing and choosing among alternatives. An agent is faced with a “crossroad,” alternative actions, multiple possible strategies, or distinct modalities of action determination

For instance, there is choice between two or more action alternatives; or a choice is made between an action of normative realization or action promising instrumental gain. Or choosing between an extreme emotional expression (emotional modality) and an instrumental one (limiting emotional expression for the purpose of gaining from another agent such as an employer). Procedures or algorithms to make individual and/or collective choices. However, on what basis? Such procedures or algorithms chooses the alternative most similar to an applicable norm or value; that is, the various alternatives are compared to the relevant norm or value, and their degree of similarity is assessed. The actors choose the most similar alternative—or the one that is ranked highest in terms of similarity.

C. DET-III: This modality entails finding or constructing one or more action alternatives in an initial phase. A second phase entails the decision to approve or accept the constructed or derived actions. In case of alternative options, the agent(s) makes an assessment and choice among the alternatives, that is uses a DET-II modality.

Because of a blockage of an established activity, or its failure to do what it is supposed to do, the agent is driven to construct or generate one or more action alternatives. Similarly, agents are engaged in creative or innovative efforts.

Note that the “determinations” DET-II and DET-III are finalized through DET-I modalities of rule following or enactment. Note also that the conception of action determination replaces the more limited notion of “decision-making” and entails, as outlined above, either “following or enacting a rule”, selecting or choosing among rules, or constructing or adopting new rules.

(9) Game transformation. Game re-structuring and transformation is conceptualized in SGT through constructive actions of game agents and/or external agents. It is based on the innovative or creative capabilities of game participants; exogenous agents also engage in shaping and reshaping games. In such “open games”, the players may restructure and transform the game, its norms, its roles, and role relationships and, thereby, the conditions of further actions and interactions. SGT agents are, in part, creative, moral and ritualistic, as well as transformative beings, in part strategic (that is, “rational” but with limited (“bounded”) rationality).

(10) Normative equilibria. In SGT, games and interaction processes result in the production and manipulation of institutions, social relationships, roles, norms—and these serve, in general, as equilibria, normative equilibria (right actions, distributive justice, etc.), which is the basis of much social regulation and order.

SGT encompasses strategic behavior, on the one hand, and routine and institutionalized activity as well as ritualistic and symbolic behavior, on the other hand.21 Of course, some interactions approach the pure or ideal ritual or symbolic; others approach the pure strategic. In addition, of course, as Goffman (1959, 1969) and also Zelizer (2012) stress, people are capable of combining ritual and strategic modalities (in some cases, possibly having to “work hard” at it or drawing on rich culturally established traditions to produce complex patterns).

In a sociological perspective, actors’ attention may be less to outcomes (as in classical game theory) than to situationally appropriate symbols and rituals. Also, actors attend to the production of a “self”, an “image”, a “self-presentation”, or a group, community, or national “identity” (Goffman 1959). For instance, actors work at producing or realizing the symbols and properties of gender (Zelizer 2012) as well as the production or realization of a particular body form, male or female, in many instances, as “attractive” as possible—with aesthetic goals in the interaction situation.

SGT encompasses theoretically in a seamless manner collaborative interactions, on the one hand, and conflict situations, on the other hand. In collaboration and other forms of cooperation, the participants share information, avoid actions that would contradict or undermine the collaborative relationship.22 In a hostile relationship (which is more than simply a “zero-sum” situation), the participants are likely to choose actions to harm one another; even at great cost to oneself or the loss of opportunities for mutual gains; in extreme cases, they reject gainful collaborative opportunities, and seek situations or to produce situations with zero-sum properties.23 When it comes to questions of the use and abuse of information, the differences are clear-cut. Collaborators are predisposed to share information—except for information about themselves or their behavior, which would undermine their mutual good-will and collaborative relation—facilitating their collaboration on relevant tasks and production processes. Although positive to one another, they may engage in “benign” forms of deception, for instance, not revealing or denying instances of hostility, deception, or performance failure. In contrast, actors having hostile relationships not only withhold information that would be helpful to the other, for instance, in avoiding harmful or risky actions. Lying, deception, and cheating are consistent with the character of the relationship (but would be incompatible with a cooperative or collaborative relationship).

Established relations are, in a SGT perspective, maintained and reproduced in interaction patterns and equilibria. Social relationships among participants in a group or organization influence, of course, the way they act vis-à-vis one another and the outcomes of their interaction.

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Established relationships even influence actors’ selection of interaction situations, or their avoidance of certain situations, or their adjusting or transforming certain situations so that they are compatible with—or match—the relationships and normative order. For example, a group of research colleagues often restructure a meeting place to be more like a seminar for peers rather than a lecture hall (unless, of course, a lecture is planned).

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When a negative interaction situation cannot be controlled or restricted by the participants, they try to “act under the circumstances” in ways appropriate to their cooperative relationships. Unless one or more decide to give up on a relationship, and bracket it. In other words, they may play the “situational” game as it should be played and bracket their friendship or kinship while the game—with its rules diverging from friendship or kinship relations—is being played.

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Earlier (Burns and Roszkowska 2005, 2006), we modeled how the norms of asymmetrical relationships, such as status relationships based on gender, education, ethnicity, professional association (including military, hospital and educational systems), indicate appropriate and equilibrium interaction behavior and outcomes, namely asymmetrical ones. Zelizer (2012) speaks in terms of the actors “conducting relational work” in order to select or produce interactions and outcomes that are compatible with the relationship—they try to find and reproduce patterns that confirm their sense of what the relationship is all about and try to maintain these patterns or practices. In general, actors try to match their interactions, for instance, economic transactions, with the “meaning of the particular relation”. “Relational work consists in creating viable matches among those meaningful relations, transactions, and media”. She continues, “In Purchase of Intimacy (2007) I note that relational work becomes especially consequential when relations resemble others that have significantly different consequences for the parties. In such cases, people make extra efforts to distinguish the relations and mark their boundaries: To the extent that two relations are easily confused, weighty in their consequences for participants, and/or significantly different in their implications for third parties, participants and third parties devote exceptional effort to marking what the relationship is and is not; distinctions among birth children, adopted children, foster children, and children taken in for day care, for instance, come to matter greatly for adult-child relations, not to mention relations to the children’s other kin”.

Notice the importance of the coherence of a group rule configuration at the same time that it is distinguished from those of other groups. The performances and practices that are generated are expected to reflect the distinctions among groups—otherwise there would be confusion and disorder (see later discussion).

Establishing new relations or changing established relations. Such a mechanism has been specified and analyzed in SGT investigations as well as conceptualized in terms of meta-processes, the exercise of meta-power and relational control (Burns et al. 1985; Burns and Hall 2012).24

In the perspective of SGT social relationships and institutional arrangements—the social rules, roles, and role relationships of groups, formal organizations, communities, networks, etc.—are continually maintained and reproduced as well as modified through group interaction and negotiation as well as social structural and ecological selectivity.25 The modifications are substantial in some instances, entailing shifts between, or transformations of, core organizing principles and particular normative rules and systems of rules (e.g., family and gender relations, the relations of the rational-legal bureaucracy, democratic forms, and market arrangements) in modem societies. Various social agents—actively and creatively engaging in such processes—determine to a greater or lesser extent which rule regime or social order is to govern a complex of relationships in a particular sphere of activity or social setting (Burns and Flam 1987). Agents with relevant commitments and vested interests struggle to maintain established systems, or to limit changes in them. Others act openly or covertly to modify, avoid or transform the systems.

At the core of the SGT framework are concepts such as norms, values and judgment processes, enabling one to describe and analyze actors’ orientations about right and wrong and good and bad in their particular interaction situations.26

The SGT approach to reforming game theory—or more precisely, formulating an alternative—emphasizes, as would be expected, the importance of taking into account and analyzing such factors as the social context, the particular social relationships, roles, and norms of the ‘actors’.These factors contribute to defining many if not most of the “rules of the game”. In such a perspective, games or interaction situations are “socially contextualized or embedded” (Burns et al. 1985; Granovetter 1985).27

In general, SGT considers a rich variety of relationships and their interaction patterns: friendship, enmity, neutral relationships, superior-subordinate relationships institutionalized in groups and organizations such as those involving leadership. Classical closed games in different socio-cultural contexts results in diverse interaction patterns and outcomes as a function of the norms of particular social relationships—and they are also common-sensical, since most know what to do or what to expect in these different relationships. In groups and organizations with well-defined solidary role relationships, participants in “zero-sum” or “PD” type situations tend to act cooperatively (and predictably) rejecting the “rational” patterns of interactions and outcomes. For instances, subordinates make sacrifices for their superiors so that interaction patterns and outcomes are congruent with their defined role relationship. If there are no options congruent with their role relationship, they are likely to try to restructure or transform the situation into one with congruent patterns—or to avoid such situations altogether.

In open game situations, actors have opportunities to individually and/or collectively develop new strategies or action opportunities. Actors in solidary relationships will tend to collaborate in solving problems-in-common. Participants in enmity relations would not tend to collaborate and work out.

Whyte in his Street Corner Society (REF) reports on ways that in a street corner gang lower status members were psychologically and socially driven to lose at bowling when playing with their higher status members—regardless of being in some cases unmistakably more capable. These patterns contributed to safeguarding the group’s social structure and ultimately the group’s very existence by acting in ways to maintain social relationships and the social order. Established status ritual and discourses typically play an important role in such social structuring work (“relational control”) (Burns and Hall 2012).

Additionally, social actors involved in a variety of interactions may purposefully avoid situations involving conflicts such as zero-sum situations because those outcomes could entail unacceptable results for self and others; this is particularly the case of actors with solidarity relationships such as, for example, friendship, as well as for those involving status or authority hierarchies as in the example above from Street Corner Society.

Informal gender interactions are typically highly codified, and do not involve a maximization of outcomes, but instead entail the use of cultural scripts and rituals to maintain a particular social relationship or order (often underlying the preservation of hegemony by one type of actor or group over another).28

These cases help us see how much complexity is involved in many forms of interaction which classical game theory lacks the language, the conceptual tools to effectively describe and analyze.29

The following sections elaborate GT and SGT conceptualizations in applications to the description and systematic differentiation of groups and organizations and their comparative analyses.

2. Elaboration of Group and Game Theories and Their Interrelationships

2.1. Group Differentiation According to Group Rule Configurations

For any given group in its material and social context, the different content rules in the universal rule categories make up stable sub-complexes—subcultures—linking, for instance, particular value/goal rules relate to involvement/recruitment rules and group identity rules as well as production and resource rules. In other words, a given group fills up the contents of the universal rule categories in its own particular ways—which has an identifiable logic.30 That is, the various content rules relate to one another systemically for a given collective.

One can envision a matrix of rule interdependencies with compatibility constraints among the rules. We refer to such interrelationships as group rule configurations (which for an established, enduring group are often social equilibria (Burns and Roszkowska 2006)).31 An important class of rule configurations entail linkages among group identity rules (category I), group purpose and value orientation rules (category III), involvement/recruitment rules for involving and socializing committed and capable actors (category II), an appropriate set of relations and roles for the tasks of accomplishing group productions/performances (V), appropriate production programs or functions for realizing or accomplishing group goals/values (VI), appropriate resources (materials and technologies) (IX) for the production functions, and appropriate/legitimate time and places to conduct these group activities (X). Table 2 presents one illustration of a rule configuration, in this case, the 9/11 terrorist group (Dermott 2005; Kean 2014; see also later).

In the following sub-section, we differentiate and compare selected groups according to their particular rules specified in the universal categories, that is, their group rule configuration.

2.2. Group Rule Configurations and Differentiation among Groups

Groups are distinguishable according to their value orientations and purpose(s) (spiritual, economic interests, artistic creation, coercive and/or sadistic engagements), social structure (for instance, hierarchical, egalitarian, mixed), basis of group involvement and commitment (e.g., normative, affinity-attraction, remunerative, coercive), resource dependence, characteristic patterns of group behavior, and impact on the environment. Group research enables the systematic identification and specification of the major contents of universal rule categories.

The conceptualization of rule configuration is operationalized for a selection of several group systems in Table 3 characterizing diverse ideal types of groups. The cases are selected for their diversity and illustrate eight rule categories for each type of group (see Section 1.2.2 and Appendix A).33 We distinguish, on the one hand, self-organizing groups (e.g., gangs, some terrorist groups, friendship groups, and many recreational groups (as well as many research teams and business “partnerships”(Columns B and D (and possibly C))), from, on the other hand, higher order constructed or “legislated” groups (military units, business units, research institutes, administrative groups and organized units at workplaces), established and maintained by a more encompassing organization and leadership (Columns A, C, D, E, F).34 Groups including alliances, intergroup, and other similar entities may be formed through negotiation among agents.

The illustrations in Table 3 are fuzzy or rough ideal types, not crisp empirical cases (for SGT’s use of concepts of fuzziness, see (Burns and Roszkowska 2001, 2004; Roszkowska and Burns 2010).35

2.3. The Coherence of Group Rule Configurations

As indicated above, a group rule configuration does not consist of randomly selected or ad hoc rules, but of rules having some minimum degree of linkage and coherence among them. The group rule configurations presented comparatively in Table 2 and Table 3 exhibit a degree of coherence imposed by its members and/or by external agents constructing the group.36 Otherwise, people would not recognize and have stable expectations about the group ideal types; and they would not be able to distinguish identities among different groups due to contradictions and confusion in group properties; the recognition aspect is important in addition to a configuration’s key role in actual group functioning.37 The coherence of a group rule configuration is essential to group social order: to its predictability, understandability, and controllability (through rule based controls) of behavior in the group. To varying degrees, groups try to establish and maintain rule coherency and stringency of implementation for purposes of constructing a predictable social order with reliability (at least for themselves and possibly for others where relevant).38

In the discussion below we focus initially on the “internal coherence” of a single group configuration. The coherence or “logic” relates to the rules of multiple categories fitting together in connection with group purpose, group identity, production functions, roles and role relationships, etc.

The first principle of coherency. The rule content of group rule configurations typically can be characterized by more or less stable, distinct coherencies or logics. In other words, the rules of a configuration are not arbitrarily determined or selected but are required to fit together into a more or less meaningful whole (although at the same time there may be gaps and degrees of inconsistency in rule configurations because the order is a “negotiated order”, involving compromises, local adaptations, etc.), it is a historical development. Each of the groups in Table 3 has a more or less coherent rule configuration in the sense that the production functions of the group and its technologies and other resources “fit” or are “appropriate” with respect to the principal group purpose and identity. Similarly, the rules relating to recruitment and involvement of members are also fitting or appropriate in such terms.40 And the “place” of group action tends to fit such ends, means, and membership.41 In general, there is a patterning or ordering of the universal rule category contents for any given group according to the principle of matching or coherency).42

Thus, the rule configuration of the military unit (see Column A in Table 3) consists of specific identity rules as well as rules that articulate group purpose and production functions together with appropriate technologies, recruitment, training, and involvement (skills, loyalties, orientation to authority), authority relations and patterns of governance, and place or location (the rules of these categories relate in expected ways to purpose).43 The rule configuration is more or less a coherent package, an identifiable, more or less orderly rule complex. Its coherence and, if you will, its performance effectiveness, varies depending on group tasks, the membership and resource bases and other variables such as the ones suggested below.

Consider a research laboratory, for instance a high-energy lab such as CERN or the Stanford Linear Accelerator (SLAC) (see column D in Table 3). Its identity rules, in addition to name, logo, and location, concern its purpose, its particular research production functions with appropriate technologies, and its rules for recruitment, training, and involvement of participants. Besides permanent scientific leadership and staff, there are selected visitors who come to CERN (or SLAC) to conduct experiments during allocated time periods, they are, in other words, temporary participants in the group, bound to accept the rule regime governing the facility.

In sum, the first principle concerns the coherence or logic of the basic group rule configuration(s). One purpose or function of a coherent group rule configuration entails making group behavior understandable, predictable and controllable in the group domain(s) of activity. It enables predictable coordinated action—and under certain conditions—more effective group actions. However, the level of rule coherence varies depending on the type of group and its main concerns (Burns et al. 2014).

There are multiple coherencies (or incoherencies as the case may be) associated with any rule regime. Other principles of coherence relating to group rule configurations concern the compatibility among multiple regime regimes applying in a group or organization, or the compatibility between a group configuration (inter-configuration coherence);44 and the compatibility between a group configuration and external agential and institutional demands deriving from the larger socio-cultural and institutional context.

2.4. Compatibility of Multiple Group Regimes

We mentioned earlier that a group may have more than one configuration—which is characteristic of groups or organizations that operate with multiple purposes and production functions, for instance in the case of a group of physicians, which has its professional functions as well as an economic or business function if they operate on a market. These two logics (and possibly more) may operate side-by-side (in a certain sense, parallel and interlinking) or may operate in sequence (phase model) or even in a multi-level fashion (where in case of incompatibility, the higher level process trumps the lower level one), that is, determines the leading or hegemonic rule logic of the complex of multiple rule configurations.

All of our illustrations (Table 3) are ostensibly single logic cases (“ideal types”), but our approach is not limited to such cases and is capable of analyzing groups with multiple group rule configurations or logics, as in the case of a professional group of physicians involved in a private health care market, so that the group operates with a professional configuration as well as a market group configuration; often these are kept distinct through a division of labor, buffering roles between the two domains, and taboos and rituals to prevent or correct any “market pollution” of the professional order (ethos), or any risky subversions of the logic of the market by professional considerations (Machado 1998; Machado and Burns 1998).

Compatibility between a group configuration and the requisites of the larger context. The question is to what extent does the group configuration “fit”, or is coherent with, a larger socio-cultural and institutional context, for example, relevant laws and strong societal norms. A group may find one or more rules in its particular rule configuration in contradiction with the demands of external social structures and/or powers.45 It may be incapable or unwilling to satisfy specific “performance” demands or legitimation requirements of the regulative environment because doing so would violate rules in its group regime—for instance, professional norms in the case of a professional group or market demands in the case of business enterprises. Neo-institutionalists stress the role of such an environment in constraining and selecting and “reproducing” certain institutional forms, making for greater similarity or convergence of institutional forms than otherwise might be expected.46 However, the extent of homogeneity will depend to a greater or lesser extent on the uniformity and force of regulation and on the uniformity and strength of predisposition to compliance among regulated groups (see discussion below concerning deviant behaviour and frontstage and backstage differentiation).

For instance, a medical practice cannot be referred to and operate as a “clinic” unless it meets certain legal, professional, and financial criteria. Similarly, the requisites of legitimation and specific performance demands apply to organizations wishing to be certified as hospitals—they have to provide designated services and maintain certain levels of professional treatment and service. This holds true in a similar fashion in cases of accreditation of a school, college, or university; a “five star” hotel, a “security service”, a company or a bank licensed to handle or operate with such dangerous chemicals such as dynamite. The external demands to a greater or lesser extent make for common rule coherency (a major factor in the institutional and cultural context) and the homogeneity of groups operating in a given regulated domain or sector.

To be certified or legitimized in such a context, a group’s operating rule regime is expected to satisfy particular criteria and to result in specified performance patterns and practices. Once again, the rule contents of the group configuration are not arbitrary but are “selected” and adapted to satisfy external institutional, legal, and legitimation requisites as well as internal coherence requirements.

Of course, some groups (the proportion varies depending on the field of action and the diverse properties of the groups) do not fit in or conform to environmental demands. They contradict or are incoherent with respect to the environmental legal and normative requisites. This may be because of a lack of sufficient resources, or agential expertise and capabilities, or the pressures to make gains and/or avoid losses through pursuing deviant strategies. This is obvious in the case of a terrorist group (column E in Table 3) but it is also true of apparently legitimate military, business, professional, or research groups that secretly betray their designated purposes and normative requisites. Any of the groups may deviate in some respects from their established “frontstage regime” and, thus, are likely to operate so as to conceal their deviance from authorities and/or publics.47 Indeed, such is true of many apparently legitimate enterprises, political parties, professional groups, universities, hospitals, etc. whose operative rule configurations and their actual realizations (that is their “back stage performances”)48 deviate to a greater or lesser extent from their front stage presentation of self and the ostensible adherence to the laws and norms applying to them (Burns and Flam 1987). Consequently, they operate to conceal their deviant activities and to carefully maintain a front stage/back stage distinction in their behaviour.

The theoretical concepts of multiple group rule configurations and incoherency shed new light on and point to new research questions about differentiation between front stage and back stage (Goffman 1959). In other words, frontstage-backstage differentiation is one form of incoherence between more or less distinct rule configurations, namely that of the frontstage normatively legitimate performance patterns and that of backstage deviation. This is one instance of the general pattern of multiple incoherent but related rule configurations—but where each configuration may be more or less internally coherent. The frontstage rule configuration is one required by law or institutional authorities, at the same time the group operates or tries to operate with a backstage rule configuration that better fits its purpose, limited resources, and/or the local context with its own incompatible pressures.

This pattern of discrepancy between what is legally and/or administratively required in the larger context and the group operative rule configuration and production activities shows up in many forms of group deviance (corruption, unprofessional and unethical behaviour, criminality, etc.).49 The concept of rule configuration coherence sheds light not only on frontstage-backstage differentiation but on Goffman’s “conman” (Goffman 1959).50 He or she (and often there is a group engaged in such systematic deception) constructs and maintains a coherent image vis-à-vis their potential victims (investors, key agents of an enterprise, or wealthy persons). At the same time, con-agents establish and maintain a secret rule configuration known only to themselves, including secret rules of deception, bookkeeping and reporting. Their secret illegal configuration dovetails at key junctures with the frontstage legal version. Money or “real” resource outputs flow into, for instance, their secret accounts—but there is dual and, of course, deceptive bookkeeping: that of the frontstage with virtual accounts and the backstage with more real accounts for use by the “con-group”. Particularly interesting from a rule system perspective is that Con-agents require coherent rules in their rule complex used to translate back and forth between the fraudulent system and the legitimizing frontstage system. Of course, the fraudsters keep the translation rules and processes known only to themselves.

The multiple mechanisms structuring group rule configurations point up the importance of an analysis of the process of determining the contents of universal rule categories that make up rule configurations. At the same time, much group rule determination involves compromises—because of internal differences among members but also because of divergence between, on the one hand, internal group rule preferences and, on the other hand, external requirements for group rules and practices.

Our approach alerts one to the fact that multiple mechanisms structure group rule configurations (that is, the selection and determination of their contents). It is not only the group itself which decides on its rules. The multiple and to a certain extent contradictory mechanisms make for incoherencies and compromises of group purposes, norms, production functions, and performances. There are some groups, of course, that operate in minimally regulated spheres or domains (or, are able to effectively avoid through institutionalized powers and/or methods of deception vis-à-vis external constraints and regulation), and they may enjoy considerable freedom and leeway to determine the rule configuration as they wish; this obviously applies to the underground and backstage-oriented groups referred to above.

2.5. Group Prioritization with Respect to Coherence: Issues of Identity, Social Order, and Its Impact on Performance and Group Outputs

Why are group actors concerned at all—and to what extent—about the coherence of their rule configurations? A further question relates to the issues about which group actors show the most concern with respect to coherency?

Coherency considerations are most likely in areas where group concerns are high concerning predictability, control/governance and social order: considerations such as, for instance, group identity and status, areas of sacrality, areas of key collective activities and performances, and security. These considerations lead to the articulation of overarching meta-rules which define or assure that the particular rules selected or determined for a rule configuration are appropriate and fitting one another (and fitting other significant rule complexes) and provide sufficient levels of coherence in one or more areas of critical importance.

Of course, some groups have relatively low rule configuration coherence and may show little or no concern about issues of coherency—for reasons identified in the following discussion. However, many groups are highly attentive to these issues; in large part because they concern matters of order and control in areas of major importance to the group.

• Identity and boundary control. If the group is highly concerned about identity issues and, in particular, distinguishing itself from other group(s), then it tries to assure coherence and implementability of recruitment, participation, and performance rules in the rule configuration relating directly (or even indirectly) to group identity. Coherency failure results in ambiguous and confusing identity, status, and performance—for example, instances of group boundary transgression and “pollution”. Performances are required to be compatible with or to realize identity.
• The boundary between “the sacred and the profane”. In areas of sacrality, a group tries to assure coherence of rule configuration(s) relating to distinctions between the sacred and the profane, and securing the appropriate behavior in relation to these distinctive domains of social action. Incoherence or ambiguity of rules leads to risks of dangerous transgressions and pollution of a sacred area. Violation of rules and rituals that play an important part in distinguishing the sacred from the profane is responded to with fury and even violence.
• Demand for highly effective collective performance. In the cases (see Table 3), the military,51 the business unit,52 and the terrorist group try to assure coherence among rules so as to assure effective group coordination and collective performance—as they relate to key concerns or purposes of such groups.53
• Risky technologies and materials. A group (concerned about its own safety) and/or the external legal and institutional environment demands are oriented to high control of, for instance, risky technology (nuclear power plant, commercial aircraft, high speed trains, etc.), dangerous materials such as hazardous chemicals and explosives. Therefore, it tries to assure appropriate and coherent rules relating directly or indirectly to effective deployment and controlled handling of the risky technologies and materials.

In general, the coherence of a group’s rule configuration is essential to group social order: predictability, understandability, and controllability (through rule based controls) of behavior in the group and control over outputs. To varying degrees, groups succeed in establishing and maintaining rule coherency and stringency of implementation for the purposes of reliable performance and predictability—and social order generally—at least in those groups concerned about social order and effective performance relative to their purpose(s) and group requisites.54

Established groups tend to develop and operate with a meta-rule or higher level commitment rule which is one of the main bases for selection and coordination of the particular rules of a configuration (such prioritizations are especially noticeable when rule adaptations or changes are necessary) (see later discussion).55 Typically, such a meta-rule is associated with group purpose and identity as well as effective functioning.56 As indicated in Table 1, Table 2 and Table 3 as well as Appendix A, identity does not concern only visible symbols but often concerns the special group purpose(s) and means of production and even its internal social structure and governance as well as locations—all playing a part in its “identity complex”. In many groups, the meta-rule of coherent design or structuration is embodied in, articulated by, and even imposed by a charismatic or powerful leader—the principal source of “group configuration design”—possibly one external to the group.

Groups may strive for coherence in key areas but fail to achieve it. The world is messy, confusing, difficult to order, because of not fully controllable internal and external forces and dynamics. For instance, regarding key group concerns specified earlier:57 Incoherencies increases the likelihood of misperception, confusion, coordination and, in general, governance problems. Examples of group and organizational problems arising from incoherence are discussed and illustrated below.

In sum, what we are claiming is that the characteristic coherence or logic of a group rule configuration is typically motivated by considerations such as identity, sacrality, effective collective action, and security. These need not always be related to ostensibly group purpose(s). However, in any case, such considerations lead to the establishment of overarching meta-rules which are oriented to defining and assuring that the particular rules selected or determined in the rule categories are appropriate for the overall rule configuration and are also appropriate or fitting for one another. However, such aims may fail resulting in cognitive-normative incoherence, confusion, disorder and performance failings.58

3. Linking Group Theory to Social Science Game Theory

This section links the two theories. The linkage is based on social rule system foundations, which is a cultural-institutional approach to group as well as game conceptualization.

We have identified a particular group subculture—group rule configuration—that characterizes an ideal type or class of groups. The configuration specifies rule regime(s), in particular, norms regarding appropriate members, their roles, group technologies and materials, group settings/places and times, production algorithms, and other group rule complexes (see Figure 2).

Group actors participating in interactions—subject to and regulated by group rule regime(s)—generate patterns of interaction and outcome. This occurs in one of the two ways specified in the game theory framework: (I) activity determination entailing following or implementing rules, rule complexes, algorithms, for instance routinized or ritualist role interactions, standard operating procedures (S.O.Ps), etc.; (II) activity determination through game choice and decision-making, that is, a proper game. Games are socially embedded in the group subculture, they tend to be played according to the norms, roles, and other rule complexes characterizing the group rule configuration or sub-culture. For instance, the military unit produces ritual interactions expressing or reinforcing status differences, thus maintaining its internal social order. Also, a business unit generates interactions distinguishing between managers and subordinates, thus maintaining its social order. In both cases, “decision-making” may be involved but the superiors make the decisions and direct subordinates to comply with them (disobedience activates explicit governance processes). Even if a subordinate is ordered or encouraged by a superior to make choices—for instance, to take an initiative, to innovate—the superior is likely to judge whether or not the choice is acceptable (Burns et al. 1985).

As a perusal of Table 3 shows, patterns of activity and interaction are already specified for each of the ideal type of groups. Many of the patterns are routine and entail predictable group behavior. However, the patterns vary substantially among groups—because group sub-cultures (i.e., rule configurations) vary. Factors that play a significant role in differentiating groups are, of course: group identity and purposes, group membership, group production functions or algorithms, and group technologies, as well as such factors as group size.59

Multiple factors make for the particular patterns characteristic of a type or class of group. Groups even in the same class or ideal type will differ to a greater or lesser extent because of external/contextual factors (the particular environments in which they function) as well as internal factors (differences in the people participating, their characteristic technologies, their particular production functions and algorithms, their governance and leadership processes, etc.). Thus, although there are rough family resemblances in the groups belonging to an ideal type, the interactions and outcomes vary because of internal and external differences—they can still be systematically compared and analyzed using our framework.

3.1. Universal Group Games

While much group behavior is relatively routine and predictable, all functioning or established groups have certain universal games, for instance, collective decision situations that are repeated, more often in some groups than others. That is, bounded free will, collective choice and less than fully predictable behavior occurs. The following is a selection of several such games:

(a)

Group collective problem-solving. This concerns non-routine problems which calls for judgment and decision-making in dealing with them. Questions such as the following confront the group: what is the problem? How to deal with it? The problem(s) may be internal ones arising in connection with new members, new leadership, new technologies, changes in resource levels, growth in group size or scale. Or, changes in key external conditions or external agents evokes group decision processes. For instance, external agent(s) on whom the group is dependent (“resource dependency”) increase demands in exchange for the resource provided or make additional demands. The group must decide how to react to the demands, for instance, whether or not to accept the demands. Negotiation may ensue, requiring further group decision-making.

Radical material change taking place in the environment—flooding, an emerging volcano, or declining food resources (as a result of overhunting or soil salinization) forces the group to abandon the area in order to survive. The group or its leadership makes decisions about departure and where to migrate to.

(b)

One universal type of group problem-solving is non-routine conflict-resolution (internal and/or external conflict). Internal conflicts may arise in connection with rivalry among leaders or ongoing hostility between some group members or subgroups. Or, it may involve conflict with external agents. Some sroups establish procedures or mechanisms to resolve non-routine conflicts such as adjudication, negotiation, and democratic vote, which they activate in such situations.

(c)

Games about changing rules, policies, paradigms. Functioning or ongoing groups sooner or later engage in games that relate to non-routine changes in group rules and policies as well as entire paradigms. That is, the change is not automatic or algorithmic but involves deliberation and choice. In these situations, there is often a vigorous situational “politics” in the group games to establish, maintain, and change social rules and complexes of rules (in groups as well as organizations and communities). Actors may disagree about, and struggle over, the definition of the situation, and thus over which rule system(s) should apply or how the rule system(s) should be interpreted or applied in the situation. Actors in any group tend to encounter resistance from others when they deviate from or seek to modify established important group rules—or even merely talk about such actions. This sets the stage for games of exercising power either to enforce rules or to resist them, or to introduce new ones. Pressure to change rules and rule complexes may also come from outside the group, for instance external legal requirements or pressures from powerful external agents. Typically, in these cases, the group will try to decide whether to accept the change requirement or oppose it, or accept it “frontstage” but operate clandestinely (“backstage”) in opposition to the external demands.

(d)

Games about internal and external governance. All functioning groups have such games. These are particularly observable in the case of non-routine deviance or breakdown in group order. Some groups have stringent governance, multiple internal controls such as in our illustrative military and terror groups concerning internal behavior such as required manifestations of loyalty and explicit adherence to key norms and role patterns.

(e)

Games of Secrecy. All groups have secrets and maintain a frontstage public position as distinct from a backstage group or subgroup position. Much concealment and deception is routine, automatic. Foror non-routine situations, however, there are well-recognized games and strategies around frontstages, back-stages, and their interconnections (Goffman 1959, 1974). Some groups emphasize or exaggerate the distinction between frontstage and backstage, especially if their performance, their freedom, their sustainability depends on concealing illegal activities, inappropriate bership, and forbidden resources and technologies This is particularly important for spy groups or groups engaged in illegal activities (e.g., criminal groups).

3.2. Differentiation in Rule Configurations and the Definition and Regulation of Games

Because group sub-cultures (characteristic rule configurations) differ, the norms and other rules that define and regulate the universal games will be different. Differences are suggested by, for instance, the Type V and VIII rule categories—norms governing forms and patterns of leadership and collective decision-making, respectively, for problem-solving and changing rules. A group leader—appointed or elected—may be in a position with (some) group support to change symbols of identity, group purpose or paradigm, its action repertoires, or modalities of collective choice. Or, a group introduces a new technology which calls for new recruitment of people to operate or to maintain the technology; or changes have to be made in performance norms/production algorithms, division of labor, application of norms of distributive justice. Groups with substantial authority and status differentiation tend to organize their universal games accordingly: for instance, the military, terrorist, prison administration, and business groups have authoritative forms for collective decision making to change a rule, role relations, or production algorithms (that is, there are asymmetry rules in contrast to the symmetry assumption of classical game theory). In research groups and many social clubs, the typical form for making decisions is either through multi-agent negotiation and/or democratic procedures (while some form of symmetry obtains, the actual negotiation or democratic forms may differ substantially depending on the particular rule regime and context applying to the group).

4. Concluding Remarks

(1)

The universal interaction grammar specifies the finite rule categories for all ongoing groups, communities, and organizations. These make up a meta-system. The specific empirical rule content of each and all categories for each group defines the characteristic rule configuration (a specific group “subculture”). That is, a configuration provides key game “rules and rule complexes” for each group. This is the linkage based on social rule system theory between group theory and social science game theory, as we have suggested here.

(2)

The group configuration is then a complex of norms and other rules providing a major part of the particular socio-cultural character and “rules of games” (game structures) for the group. Norms of purpose, norms for maintaining/reproducing identity, norms of interaction (authority relations, cooperation, rules of fairness, norms of production/performance (for instance, having fun, producing new scientific or policy knowledge, or norms for doing business and making money and also satisfying clients)). There are also norms for accounting as well as for producing group narratives; norms about appropriate places and times for group activities. Game and interaction outputs—production of patterns are often normative equilibria.

(3)

A group or organizational rule configuration coordinates actors, contributes to organizing and regulating them; it enables participants to understand what is going on, who does what (or can do what), how, why, etc. It can be used thus to simulate and to predict (as long as the rule regime continues to be applicable and to function properly); also, the regime provides a basis for the asking and giving of group and individual accounts, to criticize and penalize wayward performance and outcomes as well as to praise and reward successful group and individual behavior.

(4)

A particular group rule configuration = group subculture = distinct rule regime or norm complex. A configuration has a “cultural logic” or rationality based on the regime organizing and regulating group and individual activities and outputs/outcomes. It contributes to defining a group and differentiating it from other kinds of groups. It contributes to defining types of group interaction situations and their “rules of the game”.

(5)

All functioning groups have identity rules—at least for referring to and reflecting on group conditions and behavior. For some groups, identity—especially identity contrasted with other competing or conflicting groups—is a major group dimension. While in some groups identity rules and identity are major factors in group life, in many other groups, identity is only a name or symbol for themselves, with no special value attached to the identity, other than their attachments to the group and/or its members.

(6)

Norms of cooperation and integration are found to varying degrees in all of the groups in Table 3 (and are typical of most ongoing groups, until conflict or death and disease undermine groupness). The obvious exception in our sample of groups is the “prison social organization” where there are barriers and norms of limited cooperation; there is often even relatively intense enmity between prison guards and prisoners. Cooperation among most members of terrorist groups tend to be highly constrained since cells are meant to be kept secret from the outside world and from one another (as part of their overall clandestine functions).

(7)

All groups have to acquire and maintain their material and agential bases (their place(s), particular technologies for group existence, recruitment of new members for purposes of replacement and/or growth, and some level of financing and resource support) Some groups are high-resource consumers (energy, water, land, or financial resources); others require minimal resources for their purposes and activities. This relates, of course, to issues of group vulnerability and sustainability.