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In a Weakly Dominated Strategy Is Strength: Evolution of Optimality in Stag Hunt Augmented with a Punishment Option

Published online by Cambridge University Press:  01 January 2022

Peter Vanderschraaf
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Abstract

I explore the evolution of strategies in an Augmented Stag Hunt game that adds a punishing strategy to the ordinary Stag Hunt strategies of cooperating, which aims for optimality, and defecting, which “plays it safe.” Cooperating weakly dominates punishing and defecting is the unique evolutionarily stable strategy (ESS). Nevertheless, for a wide class of Augmented Stag Hunts, polymorphic strategies combining punishing and cooperating collectively have greater attracting power for replicator dynamics than that of the ESS. The analysis here lends theoretical support to the altruistic punishment hypothesis in the social sciences.

Type
Research Article
Information
Philosophy of Science , Volume 83 , Issue 1 , January 2016 , pp. 29 - 59
Copyright
Copyright © 2016 by the Philosophy of Science Association

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Footnotes

†.

My thanks to Russell Golman, Arnold Kim, Scott Page, and two anonymous referees for their comments on earlier versions of this article.

References

Ben-Porath, Elchanan, and Dekel, Eddie. 1992. “Signaling Future Actions and the Potential for Sacrifice.” Journal of Economic Theory 57:36–51.CrossRefGoogle Scholar
Binmore, Ken. 2006. “Why Do People Cooperate?” Politics, Philosophy, and Economics 5:81–96.CrossRefGoogle Scholar
Börgers, Tilman, and Sarin, Rajiv. 1997. “Learning through Reinforcement and Replicator Dynamics.” Journal of Economic Theory 77:1–14.CrossRefGoogle Scholar
Bowles, Samuel, and Gintis, Herbert. 2011. A Cooperative Species: Human Reciprocity and Its Evolution. Princeton, NJ: Princeton University Press.Google Scholar
Boyd, Robert, Gintis, Herbert, Bowles, Samuel, and Richerson, Peter. 2003. “The Evolution of Altruistic Punishment.” Proceedings of the National Academy of Sciences 100:3531–35.CrossRefGoogle ScholarPubMed
Ensminger, Jean, and Henrich, Joseph, eds. 2014. Experimenting with Social Norms: Fairness and Punishment in Cross-Cultural Perspective. New York: Russell Sage.Google Scholar
Gintis, Herbert, Bowles, Samuel, Boyd, Robert, and Fehr, Ernst, eds. 2005. Moral Sentiments and Material Interests: The Foundations of Cooperation in Economic Life. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Golman, Russell, and Page, Scott E. 2010a. “Basins of Attraction and Equilibrium Selection under Different Learning Rules.” Journal of Evolutionary Economics 20:49–72.CrossRefGoogle Scholar
Golman, Russell, and Page, Scott E. 2010b. “Individual and Cultural Learning in Stag Hunt Games with Multiple Actions.” Journal of Economic Behavior and Organization 73:359–76.CrossRefGoogle Scholar
Guala, Francesco. 2012. “Reciprocity: Weak or Strong? What Punishment Experiments Do (and Do Not) Demonstrate.” Behavioral and Brain Sciences 35:1–59.CrossRefGoogle ScholarPubMed
Harms, William. 1997. “Evolution and Ultimatum Bargaining.” Theory and Decision 42:147–75.CrossRefGoogle Scholar
Harsanyi, John, and Selten, Reinhard. 1988. A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press.Google Scholar
Herings, P. Jean-Jacques, and Vannetelbosch, Vincent J. 1999. “Refinements of Rationalizability for Normal-Form Games.” International Journal of Game Theory 28:53–68.CrossRefGoogle Scholar
Hofbauer, Josef, and Sigmund, Karl. 1998. Evolutionary Games and Population Dynamics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kandori, Michihiro, Mailath, George J., and Rob, Rafael. 1993. “Learning, Mutation, and Long Run Equilibria in Games.” Econometrica 61:29–56.CrossRefGoogle Scholar
Lewis, David. 1969. Convention: A Philosophical Study. Cambridge, MA: Harvard University Press.Google Scholar
Maynard Smith, John. 1982. Evolution and the Theory of Games. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Morris, Stephen. 2000. “Contagion.” Review of Economic Studies 67:57–78.CrossRefGoogle Scholar
Nash, John. 1950. “The Bargaining Problem.” Econometrica 18:155–62.CrossRefGoogle Scholar
Nash, John 1953. “Two-Person Cooperative Games.” Econometrica 21:128–40.CrossRefGoogle Scholar
Rand, David, Armao, Joseph J., Nakamaru, Mayuko, and Ohtsuki, Hisashi. 2010. “Anti-social Punishment Can Prevent the Co-evolution of Punishment and Cooperation.” Journal of Theoretical Biology 265:624–32.CrossRefGoogle ScholarPubMed
Rousseau, Jean Jacques. 1755/1977. “Discourse on the Origin or Foundations of Inequality among Men.” In The Discourses and Other Early Political Writings, ed. Gourevitch, Victor, 111–231. Cambridge: Cambridge University Press.Google Scholar
Rubinstein, Ariel. 1991. “Comments on the Interpretation of Game Theory.” Econometrica 59:909–24.CrossRefGoogle Scholar
Samuelson, Larry. 1993. “Does Evolution Eliminate Dominated Strategies?” In Frontiers of Game Theory, ed. Binmore, Ken, Kirman, Alan, and Tani, Piero, 213–35. Cambridge, MA: MIT Press.Google Scholar
Binmore, Ken, Kirman, Alan, and Tani, Piero 1997. Evolutionary Games and Equilibrium Selection. Cambridge, MA: MIT Press.Google Scholar
Sandholm, William H. 2010. Population Games and Evolutionary Dynamics. Cambridge, MA: MIT Press.Google Scholar
Sandholm, William H., Dokumaci, Emin, and Franchetti, Francisco. 2012. “Dynamo: Diagrams for Evolutionary Game Dynamics.” http://www.ssc.wisc.edu/∼whs/dynamo.Google Scholar
Schlag, Karl H. 1998. “Why Imitate, and If So, How? A Boundedly Rational Approach to Multi-armed Bandits.” Journal of Economic Theory 78:130–56.Google Scholar
Skyrms, Brian. 1994. “Evolution of an Anomaly.” Technical Report MBS 94-22, Institute for Mathematical Behavioral Sciences, University of California, Irvine.Google Scholar
Skyrms, Brian 1996. Evolution of the Social Contract. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Skyrms, Brian 2004. The Stag Hunt and the Evolution of Social Structure. Cambridge: Cambridge University Press.Google Scholar
Stalnaker, Robert. 1994. “On the Evaluation of Solution Concepts.” Theory and Decision 37:49–73.CrossRefGoogle Scholar
Stalnaker, Robert 1996. “Knowledge, Belief, and Counterfactual Reasoning in Games.” Economics and Philosophy 12:133–63.CrossRefGoogle Scholar
Sugden, Robert. 2004. The Economics of Rights, Co-operation and Welfare. 2nd ed. New York: Macmillan.Google Scholar
Taylor, Michael. 1987. The Possibility of Cooperation. Cambridge: Cambridge University Press.Google Scholar
Taylor, Michael, and Ward, Hugh. 1982. “Chickens, Whales and Lumpy Goods: Alternative Models of Public-Goods Provision.” Political Studies 30:350–70.CrossRefGoogle Scholar
Taylor, Peter, and Jonker, Leo. 1978. “Evolutionarily Stable Strategies and Game Dynamics.” Mathematical Biosciences 16:76–83.Google Scholar
Wagner, Elliot. 2012. “Evolving to Divide the Fruits of Cooperation.” Philosophy of Science 79:81–94.CrossRefGoogle Scholar
Weibull, Jörgen W. 1995. Evolutionary Game Theory. Cambridge, MA: MIT Press.Google Scholar
Young, H. Peyton. 1998. Individual Strategy and Social Structure: An Evolutionary Theory of Institutions. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar