Abstract
This paper examines the problem of inter-group cooperation using an agent-based model. Within a single, small group, reputation can be used to promote cooperation. However, reputation fails across groups when the members of the groups cannot identify each other individually. Two mechanisms have been proposed in the literature to foster inter-group cooperation: collective sanctions and in-group policing. I use an agent-based model in an evolutionary environment to determine the effectiveness of these two mechanisms. Examining them separately, I find in-group policing results in high-levels of inter-group cooperation while collective sanctions do not. When employed concurrently, collective sanctions do nothing to enhance the effectiveness of the in-group policing mechanism and may impede its functioning.
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Notes
Having agents die addresses the concern of Hart (2001) about the implausibility of the assumption used in many game-theoretical models that agents are infinitively-lived.
I am calling this parameter λ IGC , where IGC stands for in-group cheat to differentiate it from the length of other cheating tags introduced later for the two-group model.
This appears to be the same system used by the Maghribi traders. Greif (1989, p. 868) reports, “if an agent who was caught cheating operates as a merchant, coalition agents who cheated in their dealing with him will not be considered by other coalition members to have cheated.”
Because PTR is a probability, an agent’s payoff from the game are divided by 100 before being added to the initial PTR for the time period.
While perhaps not ideal, starting the population at p makes the computer code somewhat less complex. The drawback to this is that there is no possibility of reproduction in the first time period of the model since agents do not die until the end of that time period. This does not affect the results substantively. If we begin with the number of agents set close to p, these runs become indistinguishable from runs with the initial size of the population set to p after just a few time periods of the model. Setting the initial number of agents much lower than p yields results similar to those reported below, but increases the computational run-time of the model.
Page prefers the term “state-dependent process” to “Markov process.” He also refers to “stationary” rather than time-homogenous processes.
The effective number of strategies was calculated as \(\mathit{ENS} = \frac{1}{\sum_{s=1}^{32} p^{2}_{s}}\) where s is an individual strategy, 32 is the total number of strategies, and \(p^{2}_{s}\) is the square of each strategy’s proportion of the population.
Additional runs of the model with a significant number of additional time-steps showed no discernible difference from the results presented here, providing evidence the model was fully burnt-in.
The selected lengths for λ OG are 5, 10, 25, and 50. The lengths were selected to show the change in cooperation as λ OG moves from a short punishment length, through medium punishment lengths, to a fairly long punishment length.
For these 800 runs, I fix ω at .10. I made the decision to fix ω to gain better experimental control and focus on the effect of λ OG and λ OGC . The specific number of .10 was chosen after examining the results of earlier runs. .10 is approximately where the in-group policing is most effective in promoting cooperation, while it is also yields approximately the median level of cooperation for the collective sanctioning mechanism. Since one major purpose of these tests is to determine if the collective sanctioning mechanism limits the effectiveness of the in-group policing mechanism, I selected the ω that maximizes the in-group policing mechanism’s effectiveness. That this ω also produces the median level of cooperation for the across-group punishment mechanism reassures us that this is not a value likely to have unrepresentative effects.
References
Arthur W (1994) Inductive reasoning and bounded rationality. Am Econ Rev 84(2):406–411
Axelrod R (1986) An evolutionary approach to norms. Am Polit Sci Rev 80(4):1095–1111
Axelrod R (1997a) Advancing the art of simulation in the social sciences. Complexity 3(2):16–22
Axelrod R (1997b) The complexity of cooperation: agent-based models of competition and collaboration. Princeton Univ Pr, Princeton
Bolton G, Katok E, Ockenfels A (2005) Cooperation among strangers with limited information about reputation. J Public Econ 89(8):1457–1468
Collier P, Sambanis N (2002) Understanding civil war: a new agenda. J Confl Resolut 46(1):3–12
Dellarocas C (2003) The digitization of word of mouth: promise and challenges of online feedback mechanisms. Manag Sci 49(10):1407–1424
Epstein J, Axtell R (1996) Growing artificial societies. MIT Press, Cambridge
Fearon J, Laitin D (1996) Explaining interethnic cooperation. Am Polit Sci Rev 90(4):715–735
Gigerenzer G, Selten R (2002) Bounded rationality: the adaptive toolbox. MIT Press, Cambridge
Gotts N, Polhill J, Law A (2003) Agent-based simulation in the study of social dilemmas. Artif Intell Rev 19(1):3–92
Greif A (1989) Reputation and coalitions in medieval trade: evidence on the Maghribi traders. J Econ Hist 49(04):857–882
Greif A (2004) Impersonal exchange without impartial law: the community responsibility system. Chic J Int Law 5(1):107–136
Greif A (2006) The birth of impersonal exchange: the community responsibility system and impartial justice. J Econ Perspect 20(2):221–236
Hales D (2002) Group reputation supports beneficent norms. J Artif Soc Soc Simul 5(4)
Hammond R, Axelrod R (2006a) Evolution of contingent altruism when cooperation is expensive. Theor Popul Biol 6(3):333–338
Hammond R, Axelrod R (2006b) The evolution of ethnocentrism. J Confl Resolut 50(6):926–936
Hart O (2001) Norms and the theory of the firm. Univ Pa Law Rev 149(6):1701–1715
Heckathorn D (1988) Collective sanctions and the creation of prisoner’s dilemma norms. Am J Sociol 94(3):535–562
Heckathorn D (1990) Collective sanctions and compliance norms: a formal theory of group-mediated social control. Am Soc Rev, 366–384
Hoffmann R (2000) Twenty years on: the evolution of cooperation revisited. J Artif Soc Soc Simul 3(2)
Holland J, Holyoak K, Nisbett R (1989) Induction: processes of inference, learning, and discovery. MIT Press, Cambridge
Houser D, Wooders J (2006) Reputation in auctions: theory, and evidence from eBay. J Econ Manag Strategy 15(2):353–369
Izquierdo L, Izquierdo S, Galán J, Santos J (2009) Techniques to understand computer simulations: Markov chain analysis. J Artif Soc Soc Simul 12(1)
Johnson P (1999) Simulation modeling in political science. Am Behav Sci 42(10):1509–1530
Laver M, Schilperoord M (2007) Spatial models of political competition with endogenous political parties. Philos Trans B 362(1485):1711–1721
Laver M, Sergenti E (2010) Party competition: an agent-based model. Princeton University Press, Princeton
Levinson D (2003) Collective sanctions. Stanf Law Rev 56(2):345–429
Linster B (1992) Evolutionary stability in the infinitely repeated prisoners’ dilemma played by two-state Moore machines. South Econ J 58(4):880–903
Macy M, Willer R (2002) From factors to actors: computational sociology and agent-based modeling. Ann Rev Soc, 143–167
Marney J, Tarbert H (2000) Why do simulation? Towards a working epistemology for practitioners of the dark arts. J Artif Soc Soc Simul 3(4)
Masuda N (2012) Ingroup favoritism and intergroup cooperation under indirect reciprocity based on group reputation. J Theor Biol
Melnik M, Alm J (2002) Does a seller’s ecommerce reputation matter? Evidence from eBay auctions. J Ind Econ 50(3):337–349
Miceli T, Segerson K (2007) Punishing the innocent along with the guilty: the economics of individual versus group punishment. J Leg Stud 36:81–106
Milgrom P, North D et al (1990) The role of institutions in the revival of trade: the law merchant, private judges, and the champagne fairs. Econ Polit 2(1):1–23
Milinski M, Semmann D, Bakker T, Krambeck H (2001) Cooperation through indirect reciprocity: image scoring or standing strategy? Proc R Soc Lond B, Biol Sci 268(1484):2495
Miller J, Page S (2007) Complex adaptive systems: an introduction to computational models of social life. Princeton Univ Pr, Princeton
Miller W (1990) Bloodtaking and peacemaking: feud, law, and society in saga Iceland. University of Chicago Press, Chicago
Mohtashemi M, Mui L (2003) Evolution of indirect reciprocity by social information: the role of trust and reputation in evolution of altruism. J Theor Biol 223(4):523–531
Nakao K (2009) Creation of social order in ethnic conflict. J Theor Polit 21(3):365
Nowak M, Sigmund K (1998) Evolution of indirect reciprocity by image scoring. Nature 393:573–577
Nowak M, Sigmund K (2005) Evolution of indirect reciprocity. Nature 437(7063):1291–1298
Page S (2006) Path dependence. Q J Polit Sci 1(1):87–115
Reid J (1999) Patterns of vengeance: crosscultural homicide in the North American fur trade. Ninth Judicial Circuit Historical, Pasadena
Sedikides C, Schopler J, Insko CA (1998) Intergroup cognition and intergroup behavior. Psychology Press, New York
Semmann D, Krambeck H, Milinski M (2005) Reputation is valuable within and outside one’s own social group. Behav Ecol Sociobiol 57(6):611–616
Simon B (1992) The perception of ingroup and outgroup homogeneity: reintroducing the intergroup context. Eur Rev Soc Psychol 3(1):1–30
Simon H (1957) Models of man: social and rational: mathematical essays on rational human behavior in a social setting. Wiley, New York
Wedekind C, Milinski M (2000) Cooperation through image scoring in humans. Science 288(5467):850
Wilensky U (1999) Netlogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL
Wilson M (1963) Good company: a study of Nyakyusa age-villages. Beacon Press, Boston
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Appendices
Appendix A: Parameters
Parameter | Meaning | Parameterization |
---|---|---|
lambda IGC | in-group punishment length | 10 |
lambda OG | collective sanction length | 0–100 |
lambda OGC | out-group cheater punishment length | 0–100 |
α | PTR Updating parameter | .50 |
p | population size | 2601 |
Initial PTR | Probability to Reproduce at the beginning of each round | .105 |
d | Death Rate | .10 |
μ | mutation rate | .003 |
ω | Percentage of out-group interactions | .01–.25 |
τ | Tolerance | .25 |
Burn-in | Time steps to stochastic steady state | 3000 |
Appendix B: Tolerance
Fearon and Laitin suggest that one instance of cheating in an across-group interaction should set off the punishment phase of the spiral equilibrium. However, given the random assignment of agent strategies at the beginning of each run and random mutation in the reproduction process, such a strict definition of across-group cheating means that groups are always be in the sanctioning period. This gives no chance to test whether moving in and out of the sanctioning period can lead to inter-group cooperation. Therefore, I define a tolerance level, τ, which is the maximum percentage of CD outcomes in across-group interactions that a group will tolerate before sanctioning the other group. This prevents a small amount of cheating from triggering the sanctioning mechanism. In the body of the paper, τ is set to 25 percent.
Figures 13 and 14 present the results when τ is varied from 1 to 50. In all runs, τ for the groups is set equal. If τ is not equal, the group with lower tolerance tends to reproduce at a much higher rate than the other group until it almost completely dominates the system. Conditional on tolerance being equal and having only collective sanctions in place, the level of τ has no effect on the level of cooperation in the system. This somewhat surprising results should be interpreted carefully. The key point here is not that τ has no effect, but that collective sanctions do not promote cooperation regardless of τ.
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Bausch, A.W. Evolving intergroup cooperation. Comput Math Organ Theory 20, 369–393 (2014). https://doi.org/10.1007/s10588-013-9170-1
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DOI: https://doi.org/10.1007/s10588-013-9170-1