Categorization and Cooperation across Games
Round 1
Reviewer 1 Report
Poor introduction. Give more details for literature. In the last part of your introduction, you should describe your sections: In section x, we are interested in question y and we will use technic z...
In matrix (1) you consider a special case where the benefit of cooperation b=1 and the cost c=1/2. Why you did not consider the general case where b>c>0?
Section 5: very long paragraph without any pertinent outcome.
Poor discussion: Short paragraph without any conclusion. You should be pertinent and present your principal results and give interpretation.
General remark: from the introduction to the conclusion, it is very hard to understand what are the main goals from this paper.
Author Response
Poor introduction. Give more details for literature. In the last part of your introduction, you should describe your sections: In section x, we are interested in question y and we will use technic z...
*Authors' response*: We changed and extended the literature in some important aspects. First of all, we added the central literature concerning the two game types of out model - the prisoners' dilemma (PD) and the stag hunt (SH) - to the beginning of the introduction; lines 27-28. Furthermore, we connected the involved problem of cooperation to the more specific problem of the emergence of a cooperative convention, by referring to Binmore (2008); lines 29-31. Secondly, we refer to a very important work that studies the interplay between categorization and strategic interaction over a space of stag hunt games: Huyck and Stahl (2018); lines 39-40 (we discuss its relevance more concretely in the discussion section). Thirdly, we point to the fact that our work is not strongly connected to the study of behavioral spillovers (so we removed the former references to some spillover studies from the introduction), although there might be an important relation that has been experimentally detected and reported by Peysakhovich and Rand (2016); line 54. Fourthly, we added with Macy and Flache (2002) a very relevant work with respect to the results of our learning model, namely that an intermediate aspiration level supports the emergence of a behavioral pattern that is more cooperative than in any ES equilibrium; line 90. Furthermore, we added a short description of all sections; lines 93-106.
In matrix (1) you consider a special case where the benefit of cooperation b=1 and the cost c=1/2. Why you did not consider the general case where b>c>0?
*Authors' response*: Thanks for the hint, that's a good point and we should have made it more clear in the original version. On page 3 we added the general case with b, c and x, and gave arguments for why we consider the special case with b=1 and c=1/2: i) the values for b and c do not have an impact on the nature of the game space (which contains SH games for x < 1-c/b and PD games for x > 1-c/b), but solely on the position of the cutoff point between SH and PD games, and ii) we were foremost interested in a one-dimensional game space where the variable of interest is the temptation dimension x, resulting in a simple and compact representation that focuses on the essentials.
Section 5: very long paragraph without any pertinent outcome.
*Authors' response*: Due to the fact that we bundled the simulation experiments (Section 5.2) with the analysis of the results (former Section 5.3), Section 5 became indeed quite long and made the results of the experiments barely prominent. Therefore we gave the analysis a new Section (now Section 6) to highlight the final part of Section 5.2, the pertinence of the simulation results. And probably even more important, we discuss the simulation results of 5.2 with respect to a more general research question concerning the evolution of cooperative conventions in the Discussion Section 8 (see next response).
Poor discussion: Short paragraph without any conclusion. You should be pertinent and present your principal results and give interpretation.
*Authors' response*: We rewrote the discussion. We i) compare our model with respect to other studies that concern learning across games (lines 595-607), and ii) reflect our approach and our results with respect to the general idea of the emergence of cooperative conventions under cultural evolution (lines 608-631).
General remark: from the introduction to the conclusion, it is very hard to understand what are the main goals from this paper.
*Authors' response*: Admittedly, in the introduction we come very quick to model details without making clear the main goal (in a more general sense) of our study, namely to detect factors that support the emergence of cooperative conventions, and hereby particularly their cognitive foundations. We added an early paragraph to the introduction that intends to better pin down the main goal of the study (lines 26-31). Furthermore, we take up this point in the discussion section for a more coherent total picture of the study.
Reviewer 2 Report
This paper contributes to the literature that why do people cooperate more than theoretical prediction in the prisoner’s dilemma game. They introduced a mental model that people perceive the continuum interaction structures as several categories. Given this mental model, players shared the same categorization of games. While cooperation was not attained in the evolutionary stable equilibria, it was attained when agents do social learning from successful players. The contribution of this paper is that it provides an explanation of how the spillover of cooperation from coordination games to prisoner’s dilemma game can happen.
The whole paper is well structured and especially the result is explained in detail so it is easy to follow what happened in the simulation.
I suggest some additional references which investigated spillover effect in the laboratory. And, if possible, I hope authors to discuss the consistency between the result of the mental model of categorization and the mental models proposed in some of these experimental studies.
Duffy, S., & Smith, J. (2014). Cognitive load in the multi-player prisoner’s dilemma game: Are there brains in games? Journal of Behavioral and Experimental Economics, 51, 47-56. https://doi.org/10.1016/j.socec.2014.01.006
Bednar, J., Jones-Rooy, A., & Page, S. E. (2015). Choosing a future based on the past: Institutions, behavior, and path dependence. European Journal of Political Economy, 40, Part B, 312-332. https://doi.org/10.1016/j.ejpoleco.2015.09.004
Rusch, H., & Luetge, C. (2016). Spillovers from coordination to cooperation: Evidence for the interdependence hypothesis? Evolutionary Behavioral Sciences, 10(4), 284-296. https://doi.org/10.1037/ebs0000066
Knez, M., & Camerer, C. (2000). Increasing Cooperation in Prisoner’s Dilemmas by Establishing a Precedent of Efficiency in Coordination Games. Organizational Behavior and Human Decision Processes, 82(2), 194-216. https://doi.org/10.1006/obhd.2000.2882
Minor points
L223 [0,1“]” instead of “)”
L521 [z, z+0.1“]” instead of “)”
Author Response
The whole paper is well structured and especially the result is explained in detail so it is easy to follow what happened in the simulation.
I suggest some additional references which investigated spillover effect in the laboratory. And, if possible, I hope authors to discuss the consistency between the result of the mental model of categorization and the mental models proposed in some of these experimental studies.
- Duffy, S., & Smith, J. (2014).
- Bednar, J., Jones-Rooy, A., & Page, S. E. (2015).
- Rusch, H., & Luetge, C. (2016).
- Knez, M., & Camerer, C. (2000).
*Authors' response*: Thanks a lot for this suggestion and especially for the literature references. This made us burying ourselves deeper into spillover literature and get a better understanding what are the similarities and differences between the spillover effects found/discussed in experimental studies and in our model. We discuss these point in the introduction (lines 50-54), as well as in the discussion (lines 603-607).
Minor points
L223 [0,1“]” instead of “)”
L521 [z, z+0.1“]” instead of “)”
*Authors' response*: In fact in some cases we deliberately use differnt bracket types for differentiate between an open and a closed end of an interval. For example, in the given case (L223), [0,1) is right since we want to reconsider the interval for all thresholds t1 with 0 <= t1 < 1, to highlight that t1 cannot have the value 1, since it is supposed to be srictly smaller than another threshold t2 in [0,1].
Round 2
Reviewer 1 Report
Thank you to take into account my remarks and comments to improve the paper. Now, I think it is more better thank the first version.
