The theoretical and experimental research on opting out (also called conditional dissociation) in social dilemmas has concentrated on the effect this behavior has on the level of cooperation when used against defectors. The intuition behind this emphasis is based on the common property of social dilemmas that individuals are worse off the more their opponents defect. However, this article shows clearly that other opting out mechanisms are better at increasing cooperative behavior. In fact, by analyzing the stable Nash equilibria for the repeated multi-player public goods game with opting out, our results provide a strong argument that the best opting out rule is one whereby the only groups that voluntarily stay together between rounds are those that are homogeneous (i.e., those groups that are either all cooperators or all defectors), when these groups stay together for enough rounds. This outcome emerges when defectors are completely intolerant of individuals who cooperate (e.g., defectors exhibit xenophobic behavior toward cooperators) and so opt out whenever their group has a cooperator in it. The strong preference by defectors to be with like-minded individuals causes all heterogeneous groups to disband after one round.

Czech Academy of Sciences Biology Centre 370 05 Ceske Budejovice Czech Republic

Department of Mathematics Faculty of Science University of South Bohemia 370 05 Ceske Budejovice Czech Republic

Department of Mathematics Wilfrid Laurier University Waterloo ON Canada

Zobrazit více v PubMed

Dawes RM. Social dilemmas. Ann. Rev. Psychol. 1980;31:169–193. doi: 10.1146/annurev.ps.31.020180.001125. DOI

Sigmund K. The Calculus of Selfishness. Princeton: Princeton University Press; 2010.

Isaac RM, Walker JM. Nash as an organizing principle in the voluntary provision of public goods: Experimental evidence. Exp. Econ. 1998;1:191–206. doi: 10.1023/A:1009996324622. DOI

Keser C, Van Winden F. Conditional cooperation and voluntary contributions to public goods. Scand. J. Econ. 2000;102:23–39. doi: 10.1111/1467-9442.00182. DOI

Fehr E, Gachter S. Cooperation and punishment in public goods experiments. Econ. Rev. 2000;90:980–994. doi: 10.1257/aer.90.4.980. DOI

Hauert C, Monte SD, Hofbauer J, Sigmund K. Replicator dynamics for optional public good games. J. Theor. Biol. 2002;218:187–194. doi: 10.1006/jtbi.2002.3067. PubMed DOI

Lichbach MI. The repeated public goods game: A solution using tit-for-tat and the lindahl point. Theory Decis. 1992;32:133–146. doi: 10.1007/BF00134048. DOI

Offerman T. Beliefs and Decision Rules in Public Good Games: Theory and Experiments. Dordrecht: Springer; 2013.

Izquierdo SS, Izquierdo LR, Vega-Redondo F. The option to leave: Conditional dissociation in the evolution of cooperation. J. Theor. Biol. 2010;267:76–84. doi: 10.1016/j.jtbi.2010.07.039. PubMed DOI

Aktipis C. Know when to walk away: Contingent movement and the evolution of cooperation. J. Theor. Biol. 2004;231:249–260. doi: 10.1016/j.jtbi.2004.06.020. PubMed DOI

Aktipis CA. Is cooperation viable in mobile organisms? Simple Walk Away rule favors the evolution of cooperation in groups. Evol. Hum. Behav. 2011;32:263–276. doi: 10.1016/j.evolhumbehav.2011.01.002. PubMed DOI PMC

Křivan V, Cressman R. Interaction times change evolutionary outcomes: Two player matrix games. J. Theor. Biol. 2017;416:199–207. doi: 10.1016/j.jtbi.2017.01.010. PubMed DOI

Pepper JW, Smuts BB. A mechanism for the evolution of altruism among nonkin: Positive assortment through environmental feedback. Am. Nat. 2002;160:205–213. doi: 10.1086/341018. PubMed DOI

Smaldino PE, Lubell M. An institutional mechanism for assortment in an ecology of games. PLoS ONE. 2011;6:e23019. doi: 10.1371/journal.pone.0023019. PubMed DOI PMC

Zhang B-Y, et al. Opting out against defection leads to stable coexistence with cooperation. Sci. Rep. 2016;6:35902. doi: 10.1038/srep35902. PubMed DOI PMC

Deer L, Bayer R-C. Pledges of commitment and cooperation in partnerships. Games. 2016;7:4. doi: 10.3390/g7010004. DOI

Mullett TL, McDonald R, Brown GDA. Cooperation in public goods games predicts behavior in incentive-matched binary dilemmas: Evidence for stable prosociality. Econ. Iquiry. 2020;58:67–85. doi: 10.1111/ecin.12796. DOI

Hofbauer J, Sigmund K. Evolutionary Games and Population Dynamics. Cambridge: Cambridge University Press; 1998.

Kurokawa S. Three-player repeated games with an opt-out option. J. Theor. Biol. 2019;480:13–22. doi: 10.1016/j.jtbi.2019.07.012. PubMed DOI

Fujiwara-Greve T, Okuno-Fujiwara M. Voluntarily separable repeated prisoner’s dilemma. Rev. Econ. Stud. 2009;76:993–1021. doi: 10.1111/j.1467-937X.2009.00539.x. DOI

Wardil L, Amaral MA. Cooperation in public goods games: Stay, but not for too long. Games. 2017;8:35. doi: 10.3390/g8030035. DOI

Lange PAMV, et al. Reward and Punishment in Social Dilemmas. Oxford: Oxford University Press; 2014.

Broom M, Cressman R, Křivan V. Revisiting the “fallacy of averages” in ecology: Expected gain per unit time equals expected gain divided by expected time. J. Theor. Biol. 2019;483:109993. doi: 10.1016/j.jtbi.2019.109993. PubMed DOI

Dimick M, Rueda D, Stegmueller D. Models of other-regarding preferences, inequality, and redistribution. Ann. Rev. Polit. Sci. 2018;21:441–460. doi: 10.1146/annurev-polisci-091515-030034. DOI

Wu J. Labelling, homophily and preference evolution. Int. J. Game Theory. 2020;49:1–22. doi: 10.1007/s00182-019-00672-6. DOI

Brandt MJ, Reyna C, Chambers JR, Crawford JT, Wetherell G. The ideological-conflict hypothesis: Intolerance among both liberals and conservatives. Curr. Dir. Psychol. Sci. 2014;23:27–34. doi: 10.1177/0963721413510932. DOI

Brandt, M. J., Wetherell, G. & Crawford, J. T. Moralization and intolerance of ideological outgroups. In Social psychology of morality, 18th Sydney Symposium of Social Psychology, 2 Park sq, Milton Park, Abingdon OX14 4RN, Oxford, England, 239–256 (eds Forgas, J. P., Jussim, L., & VanLange, P.A.M.) (Routledge, 2016).

Hanania R. Are liberal governments more cooperative? Voting trends at the UN in five anglophone democracies. J. Conflict Resol. 2019;63:1403–1432. doi: 10.1177/0022002718794848. DOI

Koger G, Masket S, Noel H. Cooperative party factions in American politics. Am. Polit. Res. 2010;38:33–53. doi: 10.1177/1532673X09353509. DOI

Chaudhuri, A. (ed.) Recent Advances in Experimental Studies of Social Dilemma Games (MDPI AG, Basel, Switzerland, 2016).

Ledyard JO. Public goods: A survey of experimental research. In: Kagel JH, editor. The Handbook of Experimental Economics. Princeton: Princeton University Press; 1995.

Wardil L, Silva IR, da Silva JKL. Positive interactions may decrease cooperation in social dilemma experiments. Sci. Rep. 2019;9:1017. doi: 10.1038/s41598-018-37674-5. PubMed DOI PMC

Cressman R, Křivan V. Bimatrix games that include interaction times alter the evolutionary outcome: The Owner-Intruder game. J. Theor. Biol. 2019;460:262–273. doi: 10.1016/j.jtbi.2018.10.033. PubMed DOI

Garay J, Csiszár V, Móri TF. Evolutionary stability for matrix games under time constraints. J. Theor. Biol. 2017;415:1–12. doi: 10.1016/j.jtbi.2016.11.029. PubMed DOI

Garay J, Cressman R, Móri TF, Varga T. The ESS and replicator equation in matrix games under time constraints. J. Math. Biol. 2018;76:1951–1973. doi: 10.1007/s00285-018-1207-0. PubMed DOI

Křivan V, Galanthay T, Cressman R. Beyond replicator dynamics: From frequency to density dependent models of evolutionary games. J. Theor. Biol. 2018;455:232–248. doi: 10.1016/j.jtbi.2018.07.003. PubMed DOI

Wofram S. Mathematica: A system for doing mathematics by computer. ReadingReading: Addison-Wesley; 1991.

Aksoy O. Effects of heterogeneity and homophily on cooperation. Soc. Psychol. Q. 2015;78:324–344. doi: 10.1177/0190272515612403. DOI

Altemeyer, B. The Authoritarians. 2006. https://www.theauthoritarians.org.

Wikipedia contributors. Right-wing authoritarianism—Wikipedia, the free encyclopedia. https://en.wikipedia.org/w/index.php?title=Right-wing_authoritarianism&oldid=971353989, 2020. Online; accessed 7 Aug 2020.