Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-27T17:08:21.975Z Has data issue: false hasContentIssue false
  • English
  • Français

The Evolutionary Stability of Cooperation

Published online by Cambridge University Press:  01 August 2014

Jonathan Bendor  and
Piotr Swistak
Jonathan Bendor
Affiliation:
Stanford University
Piotr Swistak
Affiliation:
University of Maryland
Get access Rights & Permissions [Opens in a new window]

Abstract

Is cooperation without central authority stable? If so, how robust is it? Despite what might be the conventional wisdom, The Evolution of Cooperation did not solve this problem deductively. In fact, results obtained later by others seem to have contradicted the book's main message. Reexamining this exceptionally influential work yields a new picture. Part of Axelrod's evolutionary story turns out to be false. But the main intuition, that retaliatory strategies of conditional cooperation are somehow advantaged, proves correct in one specific and significant sense: Under a standard evolutionary dynamic these strategies require the minimal frequency to stabilize. Hence, they support the most robust evolutionary equilibrium: the easiest to reach and retain. Moreover, the less efficient a strategy, the larger is its minimal stabilizing frequency; Hobbesian strategies of pure defection are the least robust. Our main theorems hold for a large class of games that pose diverse cooperation problems: prisoner's dilemma, chicken, stag hunt, and many others.

Type
Articles
Information
American Political Science Review , Volume 91 , Issue 2 , June 1997 , pp. 290 - 307
Copyright
Copyright © American Political Science Association 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Axelrod, Robert. 1980. “Effective Choice in the Prisoner's Dilemma.” Journal of Conflict Resolution 24(03):3–25.CrossRefGoogle Scholar
Axelrod, Robert. 1981. “The Emergence of Cooperation among Egoists.” American Political Science Review 75(06):306–18.CrossRefGoogle Scholar
Axelrod, Robert. 1984. The Evolution of Cooperation. Basic Books:New York.Google Scholar
Axelrod, Robert, and D'Ambrosio, Lisa. 1994. “Annotated Bibliography on The Evolution of Cooperation.” University of Michigan: Ann Arbor. Typescript.Google Scholar
Axelrod, Robert, and Dion, Douglas. 1987. “Annotated Bibliography on The Evolution of Cooperation.” University of Michigan: Ann Arbor. Typescript.Google Scholar
Axelrod, Robert, and Dion, Douglas. 1988. “The Further Evolution of Cooperation.” Science 242(December 9):1385–90.Google Scholar
Axelrod, Robert, and Hamilton, William. 1981. “The Evolution of Cooperation.” Science 211(March 27):1390–6.Google Scholar
Banks, Jeffrey, and Sundaram, Rangarajan. 1989. “Repeated Games, Finite Automata, and Complexity.” Games and Economic Behavior 2(06):97–117.Google Scholar
Bendor, Jonathan. 1993. “Uncertainty and the Evolution of Cooperation.” Journal of Conflict Resolution 37(12):709–34.Google Scholar
Bendor, Jonathan, and Swistak, Piotr. 1992. “Characterization of Solution Concepts in Standard Evolutionary Games.” Graduate School of Business: Stanford University. Typescript.Google Scholar
Bendor, Jonathan, and Swistak, Piotr. 1993. “Cooperation and the Evolution of Norms.” Presented at the annual meetings of the American Political Science Association, Washington, D.C.Google Scholar
Bendor, Jonathan, and Swistak, Piotr. 1995. “Types of Evolutionary Stability and the Problem of Cooperation.” Proceedings of the National Academy of Sciences 92(04 11):3596–3600.Google Scholar
Bendor, Jonathan, and Swistak, Piotr. 1996a. “The Controversy about the Evolution of Cooperation and the Evolutionary Roots of Social Institutions.” In Social Agency, ed., Gasparski, W., Mlicki, M., and Banathy, B.. New Brunswick, N.J.: Transaction Publishers.Google Scholar
Bendor, Jonathan, and Swistak, Piotr. 1996b. “Finite Automata, Trembles, Bounded Rationality, and the Evolution of Cooperation.” Graduate School of Business: Stanford University. Typescript.Google Scholar
Bendor, Jonathan, and Swistak, Piotr. 1996c. “Identifying, Characterizing, and Interpreting Evolutionary Equilibria.” Graduate School of Business: Stanford University. Typescript.Google Scholar
Binmore, Kenneth, and Samuelson, Larry. 1992. “Evolutionary Stability in Repeated Games Played by Finite Automata.” Journal of Economic Theory 57(08):278–305.Google Scholar
Binmore, Kenneth, and Samuelson, Larry. 1994. “Muddling Through: Noisy Equilibrium Selection.” SSRI Working Paper #9410. Madison: University of Wisconsin.Google Scholar
Bomze, I. M., and van Damme, Eric. 1992. “A Dynamical Characterization of Evolutionarily Stable States.” Annals of Operations Research 37(08):229–44.Google Scholar
Boyd, Robert. 1989. “Mistakes Allow Evolutionary Stability in the Repeated Prisoner's Dilemma Game.” Journal of Theoretical Biology 136(01):47–56.CrossRefGoogle ScholarPubMed
Boyd, Robert, and Lorberbaum, Jeffrey. 1987. “No Pure Strategy Is Evolutionarily Stable in the Repeated Prisoner's Dilemma Game.” Nature 327(05 7):58–59.Google Scholar
Boyd, Robert, and Richerson, Peter. 1992. “Punishment Allows the Evolution of Cooperation (or Anything Else) in Sizable Groups.” Ethology and Sociobiology 13(05):171–95.Google Scholar
Cabrales, Antonio. 1993. “Stochastic Replicator Dynamics.” Economics Working Paper 54. Barcelona: Universitat Pompeu Fabra.Google Scholar
Chisholm, Donald. 1989. Coordination without Hierarchy. Berkeley: University of California Press.Google Scholar
Dawkins, Richard. 1989. The Selfish Gene. Oxford: Oxford University Press.Google Scholar
Dekel, Eddie, and Scotchmer, Suzanne. 1992. “On the Evolution of Optimizing Behavior.” Journal of Economic Theory 57(08): 392–406.Google Scholar
Ellison, Glenn. 1993. “Learning, Local Interaction, and Coordination.” Econometrica 61(09): 1047–71.Google Scholar
Farrell, Joseph, and Ware, Roger. 1989. “Evolutionary Stability in the Repeated Prisoner's Dilemma.” Theoretical Population Biology 36(10):161–6.Google Scholar
Foster, Dean, and Young, Peyton. 1990. “Stochastic Evolutionary Game Dynamics.” Theoretical Population Biology 38(10): 219–32.Google Scholar
Friedman, Daniel. 1991. “Evolutionary Games in Economics.” Econometrica 59(05):637–66.Google Scholar
Fudenberg, Drew, and Harris, Christopher. 1992. “Evolutionary Dynamics in Games with Aggregate Shocks.” Journal of Economic Theory 57(08):420–41.Google Scholar
Fudenberg, Drew, and Maskin, Eric. 1990. “Evolution and Cooperation in Noisy Repeated Games.” American Economic Review 80(05):274–79.Google Scholar
Fudenberg, Drew, and Maskin, Eric. 1993. “Evolution and Repeated Games.” Nobel Symposium on Game Theory. Karlskog: Sweden.Google Scholar
Gale, John, Binmore, Kenneth, and Samuelson, Larry. 1995. “Learning to be Imperfect: The Ultimatum Game.” Games and Economic Behavior 8(01):56–90.CrossRefGoogle Scholar
Heclo, Hugh. 1977. A Government of Strangers. Washington, DC: Brookings Institution.Google Scholar
Hirshleifer, David, and Rasmusen, Eric. 1989. “Cooperation in a Repeated Prisoners' Dilemma with Ostracism.” Journal of Economic Behavior and Organization 12(08):87–106.CrossRefGoogle Scholar
Hirshleifer, Jack, and Coll, Juan Carlos Martinez. 1988. “What Strategies Can Support the Evolutionary Emergence of Cooperation?” Journal of Conflict Resolution 32(06):367–98.Google Scholar
Hofbauer, Josef, and Sigmund, Karl. 1988. The Theory of Evolution and Dynamical Systems. Cambridge: Cambridge University Press.Google Scholar
Kandori, Michihiro, Mailath, George J., and Rob, Rafael. 1993. “Learning, Mutation, and Long-Run Equilibria in Games.” Econometrica 61(01):29–56.CrossRefGoogle Scholar
Lorberbaum, Jeffrey. 1994. “No Strategy Is Evolutionarily Stable in the Repeated Prisoner's Dilemma.” Journal of Theoretical Biology. 168(05):117–30.Google Scholar
Mailath, George J. 1992. “Introduction: Symposium on Evolutionary Game Theory.” Journal of Economic Theory 57(08):259–77.CrossRefGoogle Scholar
March, James, and Simon, Herbert. 1958. Organizations. New York: Wiley.Google Scholar
Matthews, Donald. 1960. U.S. Senators and Their World. Chapel Hill: University of North Carolina Press.Google Scholar
Maynard Smith, John. 1982. Evolution and the Theory of Games. Cambridge: Cambridge University Press.Google Scholar
Milgrom, Paul, North, Douglass, and Weingast, Barry. 1990. “The Role of Institutions in the Revival of Trade.” Economics and Politics 2(03):1–23.Google Scholar
Milinski, Manfred. 1987. “TIT FOR TAT in Sticklebacks and the Evolution of Cooperation.” Nature 325(01 29):433–5.CrossRefGoogle ScholarPubMed
Myerson, Roger, Pollock, Gregory, and Swinkels, Jeroen. 1991. “Viscous Population Equilibria.” Games and Economic Behavior 3(02):101–9.Google Scholar
Nachbar, John. 1990. “‘Evolutionary’ Selection Dynamics in Games: Convergence and Limit Properties.” International Journal of Game Theory 19(1):59–89.Google Scholar
Oye, Kenneth. 1986. “Explaining Cooperation under Anarchy.” In Cooperation under Anarchy, ed. Oye, K., Princeton: Princeton University Press.CrossRefGoogle Scholar
Peck, Joel R. 1993. “Friendship and the Evolution of Cooperation.” Journal of Theoretical Biology 162(2):195–228.Google Scholar
Pollock, Gregory. 1988. “Population Structure, Spite, and the Iterated Prisoner's Dilemma.” American Journal of Physical Anthropology 77(4):459–69.CrossRefGoogle Scholar
Raub, Werner, and Weesie, Jeroen. 1990. “Reputation and Efficiency in Social Interactions: An Example of Network Effects.” American Journal of Sociology 96(11):626–54.Google Scholar
Rubinstein, Ariel. 1986. “Finite Automata Play the Repeated Prisoner's Dilemma.” Journal of Economic Theory 39(06):83–96.CrossRefGoogle Scholar
Schlag, Karl. 1994. “Why Imitate, and if so, How?” Discussion Paper No. B-296. Bonn: University of Bonn.Google Scholar
Schuster, Peter, and Sigmund, Karl. 1983. “Replicator Dynamics.” Journal of Theoretical Biology 100(02 7):533–8.Google Scholar
Selten, Reinhard. 1983. “Evolutionary Stability in Extensive 2-Person Games.” Mathematical Social Sciences 5(03):269–363.Google Scholar
Selten, Reinhard, and Hammerstein, Peter. 1984. “Gaps in Harley's Argument on Evolutionary Stable Learning Rules and in the Logic of ‘Tit for Tat.”” The Behavioral and Brain Sciences 7(March): 115–6.Google Scholar
Shils, Edward, and Janowitz, Morris. 1948. “Cohesion and Disintegration of the Wehrmacht in World War II.” Public Opinion Quarterly 12(Summer):280–315.Google Scholar
Snidal, Duncan. 1991. “Relative Gains and the Pattern of International Cooperation.” American Political Science Review 85(09):701–26.Google Scholar
Sobel, Joel. 1993. “Evolutionary Stability and Efficiency.” Economic Letters 42(2–3):301–12.Google Scholar
Sugden, Robert. 1986. The Economics of Rights, Co-operation and Welfare. Oxford: Basil Blackwell.Google Scholar
Sugden, Robert. 1988. “Evolutionarily Stable Strategies in the Prisoner's Dilemma and Chicken Games.” In Compromise, Negotation and Group Decision, ed. Munier, Bertrand and Shakun, Melvin. Dordrecht, The Netherlands: Reidel.Google Scholar
Sugden, Robert. 1989. “Spontaneous Order.” Journal of Economic Perspectives 3(Fall):85–97.Google Scholar
Swistak, Piotr. 1989. “How to Resist Invasion in the Repeated Prisoner's Dilemma Game.” Behavioral Science 34(04):151–3.Google Scholar
Trivers, Robert. 1985. Social Evolution. Menlo Park, CA: Benjamin Cummings.Google Scholar
Vanberg, Viktor, and Congleton, Roger. 1992. “Rationality, Morality, and Exit.” American Political Science Review 86(06):418–31.Google Scholar
Warneryd, Karl. 1993. “Cheap Talk, Coordination, and Evolutionary Stability.” Games and Economic Behavior 5(10):532–46.Google Scholar
Weibull, Jorgen. 1995. Evolutionary Game Theory. Cambridge, MA: MIT Press.Google Scholar
Wilkinson, Gerald. 1984. “Reciprocal Food Sharing in the Vampire Bat.” Nature 308(03 8):181–4.Google Scholar
Young, Peyton. 1993a. “The Evolution of Conventions.” Econometrica 61(01):57–84.Google Scholar
Young, Peyton. 1993b. “An Evolutionary Model of Bargaining.” Journal of Economic Theory 59(02):145–68.Google Scholar
Young, Peyton, and Foster, Dean. 1991. “Cooperation in the Short and in the Long Run.” Games and Economic Behavior 3(02):145–56.Google Scholar
Submit a response

Comments

No Comments have been published for this article.