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Recent Advances in Game and Decision Theory: Structures, Models, Applications...
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Recent Advances in Game and Decision Theory: Structures, Models, Applications and Software Implementation

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 October 2018) | Viewed by 20202

Special Issue Editor

Prof. Dr. David Carfì

E-Mail Website
Guest Editor
Department of Mathematics, University of California Riverside, Riverside, CA 92521, USA
Interests: mathematical economics; game theory; decision theory; risk management; bargaining theory; finance; econophysics; quantum finance; foundations of quantum mechanics; relativistic quantum mechanics; Schwartz distribution theory; differential manifolds; relativity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This special issue of the MDPI Journal “Mathematics” desires to collect research and survey papers about Game Theory and Decision Theory, from the wide range of these two fields. In particular, papers devoted to significant applications in economics, finance, industrial organization and other various concrete fields are especially welcome as well as papers in which the problem solving requires software implementations, automatic numerical calculus and renowned softwares such as Matlab, Mathematica and so on.

Game theory revealed a major method used in mathematical economics and business administration for modelling competing behaviours of interacting agents. We welcome applications in a wide range of economic phenomena and approaches, such as: auctions, bargaining, mergers & acquisitions, co-opetition, pricing, fair division, duopolies, oligopolies, social network formation, agent-based computational economics, general equilibrium, mechanism design, voting systems, experimental economics, behavioral economics, information economics, industrial organization, political economy and so on.

Papers with interrelations among different approaches to the above themes, with particular emphasis on econophysics, quantum mechanics and statistical physics approaches, are equally welcome.

Prof. Dr. David Carfì
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Game Theory
  • Decision Theory
  • Evolutionary Games
  • Bayesian Games
  • Finance
  • Microeconomics and Macroeconomics
  • Political Economics
  • Econophysics
  • Statistical Economics
  • Potential Games

Published Papers (6 papers)

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Research

19 pages, 249 KiB  
Article
Cournot-Bayesian General Equilibrium: A Radon Measure Approach
by David Carfì and Alessia Donato
Mathematics 2019, 7(1), 10; https://doi.org/10.3390/math7010010 - 22 Dec 2018
Cited by 3 | Viewed by 2579
Abstract
In this paper, we consider a Cournot duopoly, in which any firm does not know the marginal costs of production of the other player, as a Bayesian game. In our game, the marginal costs depend on two infinite continuous sets of states of [...] Read more.
In this paper, we consider a Cournot duopoly, in which any firm does not know the marginal costs of production of the other player, as a Bayesian game. In our game, the marginal costs depend on two infinite continuous sets of states of the world. We shall study, before the general case, an intermediate case in which only one player, the second one, shows infinitely many types. Then, we shall generalize to the case in which both players show infinitely many types depending on the marginal costs, where the marginal costs are given by the nature and each actual marginal cost is known only by the respective player. We find, in both cases, the general Nash equilibrium. Full article
(This article belongs to the Special Issue Recent Advances in Game and Decision Theory: Structures, Models, Applications and Software Implementation)
17 pages, 2055 KiB  
Article
Coopetitive Games for Management of Marine Transportation Activity: A Study Case
by Alessia Donato, David Carfì and Beatrice Blandina
Mathematics 2018, 6(12), 322; https://doi.org/10.3390/math6120322 - 12 Dec 2018
Cited by 3 | Viewed by 2619
Abstract
In this paper, we will use coopetitive game theory to analyze a case of real coopetition among port companies, for what concerns loading and unloading of goods, within a competitive management scenario of marine transportation activities. Our research consists of the analysis of [...] Read more.
In this paper, we will use coopetitive game theory to analyze a case of real coopetition among port companies, for what concerns loading and unloading of goods, within a competitive management scenario of marine transportation activities. Our research consists of the analysis of a study case involving coopetition between two real companies from which we obtained the financial and contractual data allowing us to define two modeling payoff functions, both of them based on real agreements and tariffs. We recognize actual coopetition and an asymmetric R&D alliance in this type of agreement, where a bigger enterprise deals with a smaller competitor, in order to capture more value from their activities. In particular, our model will show a precise coopetitive bi-dimensional trajectory within which we suggest, after a quantitative analysis, different kinds of solutions: the purely coopetitive solution, a Kalai-Smorodinsky solution and, finally, a transferable utility Kalai-Smorodinsky solution. Our methods provide specific strategy procedures determining win-win solutions for both. Full article
(This article belongs to the Special Issue Recent Advances in Game and Decision Theory: Structures, Models, Applications and Software Implementation)
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26 pages, 313 KiB  
Article
Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs
by Hsien-Chung Wu
Mathematics 2018, 6(11), 255; https://doi.org/10.3390/math6110255 - 16 Nov 2018
Cited by 4 | Viewed by 2033
Abstract
Cooperative games endowed with interval-valued payoffs are studied in this paper. Based on the interval-valued payoff and the different types of orderings, we can propose many types of so-called interval-valued cores and interval-valued dominance cores. The main issue of this paper is to [...] Read more.
Cooperative games endowed with interval-valued payoffs are studied in this paper. Based on the interval-valued payoff and the different types of orderings, we can propose many types of so-called interval-valued cores and interval-valued dominance cores. The main issue of this paper is to establish the equalities of different types of interval-valued cores and interval-valued dominance cores under a mild assumption. Without considering the individual rationality, we also establish the equalities of different types of interval-valued pre-cores and interval-valued dominance pre-cores without any extra assumptions. Full article
(This article belongs to the Special Issue Recent Advances in Game and Decision Theory: Structures, Models, Applications and Software Implementation)
27 pages, 394 KiB  
Article
Methods for Multiple Attribute Decision Making with Interval-Valued Pythagorean Fuzzy Information
by Zengxian Li, Guiwu Wei and Hui Gao
Mathematics 2018, 6(11), 228; https://doi.org/10.3390/math6110228 - 29 Oct 2018
Cited by 53 | Viewed by 2938
Abstract
Interval-valued Pythagorean fuzzy numbers (IVPFNs) can easily describe the incomplete and indeterminate information by degrees of membership and non-membership, and the Hamy mean (HM) operator and dual HM (DHM) operators are a good tool for dealing with multiple attribute decision making (MADM) problems [...] Read more.
Interval-valued Pythagorean fuzzy numbers (IVPFNs) can easily describe the incomplete and indeterminate information by degrees of membership and non-membership, and the Hamy mean (HM) operator and dual HM (DHM) operators are a good tool for dealing with multiple attribute decision making (MADM) problems because it can capture the interrelationship among the multi-input arguments. Motivated by the studies regarding the HM operator and dual HM operator, we expand the HM operator and dual HM (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs) and then to solve the MADM problems. Firstly, we propose some HM and DHM operators with IVPFNs. Moreover, we present some new methods to solve MADM problems with the IVPFNs. Finally, an applicable example is given. Full article
(This article belongs to the Special Issue Recent Advances in Game and Decision Theory: Structures, Models, Applications and Software Implementation)
45 pages, 436 KiB  
Article
Approaches to Multiple Attribute Decision Making with Interval-Valued 2-Tuple Linguistic Pythagorean Fuzzy Information
by Jie Wang, Guiwu Wei and Hui Gao
Mathematics 2018, 6(10), 201; https://doi.org/10.3390/math6100201 - 13 Oct 2018
Cited by 75 | Viewed by 3776
Abstract
The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among multi-input arguments. [...] Read more.
The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among multi-input arguments. Motivated by the ideal characteristic of the MSM operator, in this paper, we expand the MSM operator, generalized MSM (GMSM), and dual MSM (DMSM) operator with interval-valued 2-tuple linguistic Pythagorean fuzzy numbers (IV2TLPFNs) to propose the interval-valued 2-tuple linguistic Pythagorean fuzzy MSM (IV2TLPFMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted MSM (IV2TLPFWMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy GMSM (IN2TLPFGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted GMSM (IV2TLPFWGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy DMSM (IN2TLPFDMSM) operator, Interval-valued 2-tuple linguistic Pythagorean fuzzy weighted DMSM (IV2TLPFWDMSM) operator. Then the multiple attribute decision making (MADM) methods are developed with these three operators. Finally, an example of green supplier selection is used to show the proposed methods. Full article
(This article belongs to the Special Issue Recent Advances in Game and Decision Theory: Structures, Models, Applications and Software Implementation)
29 pages, 9169 KiB  
Article
Acquisition War-Gaming Technique for Acquiring Future Complex Systems: Modeling and Simulation Results for Cost Plus Incentive Fee Contract
by Tien M. Nguyen, Hien T. Tran, Andy T. Guillen, Tung X. Bui and Sumner S. Matsunaga
Mathematics 2018, 6(3), 43; https://doi.org/10.3390/math6030043 - 14 Mar 2018
Cited by 3 | Viewed by 5139
Abstract
This paper provides a high-level discussion and propositions of frameworks and models for acquisition strategy of complex systems. In particular, it presents an innovative system engineering approach to model the Department of Defense (DoD) acquisition process and offers several optimization modules including simulation [...] Read more.
This paper provides a high-level discussion and propositions of frameworks and models for acquisition strategy of complex systems. In particular, it presents an innovative system engineering approach to model the Department of Defense (DoD) acquisition process and offers several optimization modules including simulation models using game theory and war-gaming concepts. Our frameworks employ Advanced Game-based Mathematical Framework (AGMF) and Unified Game-based Acquisition Framework (UGAF), and related advanced simulation and mathematical models that include a set of War-Gaming Engines (WGEs) implemented in MATLAB statistical optimization models. WGEs are defined as a set of algorithms, characterizing the Program and Technical Baseline (PTB), technology enablers, architectural solutions, contract type, contract parameters and associated incentives, and industry bidding position. As a proof of concept, Aerospace, in collaboration with the North Carolina State University (NCSU) and University of Hawaii (UH), successfully applied and extended the proposed frameworks and decision models to determine the optimum contract parameters and incentives for a Cost Plus Incentive Fee (CPIF) contract. As a result, we can suggest a set of acquisition strategies that ensure the optimization of the PTB. Full article
(This article belongs to the Special Issue Recent Advances in Game and Decision Theory: Structures, Models, Applications and Software Implementation)
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