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Evolution of Strategies in Repeated Games with Discounting

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  • Matthijs van Veelen

    ()
    (Universiteit van Amsterdam)

Abstract

In repeated games there is in general a large set of equilibria. We also know that in the repeated prisoners dilemma there is a profusion of neutrally stable strategies, but no strategy that is evolutionarily stable. This paper investigates whether and how neutrally stable strategies can be upset in a process of mutation and selection. While neutral stability excludes that mutants have a selective advantage themselves, it does not rule out the possibility that mutants that are neutral can enter a population and create a selective advantage for a second mutant. This will be called an indirect invasion and the central results show that, for high enough continuation probability, there is no strategy that is robust against indirect invasions. Such stepping stone paths out of equilibrium generally exist both in the direction of more and in the direction of less cooperation.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-115/1.

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Date of creation: 04 Jan 2007
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Handle: RePEc:dgr:uvatin:20060115

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Related research

Keywords: Repeated games; evolutionary stability; robust against indirect invasions.;

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  1. D. Fudenberg & E. Maskin, 2010. "Evolution and Cooperation in Noisy Repeated Games," Levine's Working Paper Archive 546, David K. Levine.
  2. Samuelson, Larry & Swinkels, Jeroen M., 2003. "Evolutionary stability and lexicographic preferences," Games and Economic Behavior, Elsevier, vol. 44(2), pages 332-342, August.
  3. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Wiley Blackwell, vol. 38(113), pages 1-12, January.
  4. Robert J. Aumann & Lloyd S. Shapley, 1992. "Long Term Competition-A Game Theoretic Analysis," UCLA Economics Working Papers 676, UCLA Department of Economics.
  5. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
  6. Jonathan Bendor & Piotr Swistak, 1998. "Evolutionary Equilibria: Characterization Theorems and Their Implications," Theory and Decision, Springer, vol. 45(2), pages 99-159, October.
  7. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation-proof equilibrium: Reply," Journal of Economic Theory, Elsevier, vol. 49(2), pages 376-378, December.
  8. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
  9. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
  10. van Damme,Eric, 1986. "Renegotiation-proof equilibria in repeated Prisoner`s dilemma," Discussion Paper Serie A 84, University of Bonn, Germany.
  11. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
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Cited by:
  1. Matthijs van Veelen & Julian Garcia, 2012. "In and out of Equilibrium II: Evolution in Repeated Games with Discounting and Complexity Costs," Tinbergen Institute Discussion Papers 12-089/I, Tinbergen Institute.
  2. Heller, Yuval, 0. "Three steps ahead," Theoretical Economics, Econometric Society.
  3. Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.

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