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In and out of Equilibrium II: Evolution in Repeated Games with Discounting and Complexity Costs

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Author Info

  • Matthijs van Veelen

    (University of Amsterdam)

  • Julian Garcia

    (Max-Planck-Institute for Evolutionary Biology)

Abstract

We explore evolutionary dynamics for repeated games with small, but positive complexity costs. To understand the dynamics, we extend a folk theorem result by Cooper (1996) to continuation probabilities, or discount rates, smaller than 1. While this result delineates which payoffs can be supported by neutrally stable strategies, the only strategy that is evolutionarily stable, and has a uniform invasion barrier, is All D. However, with sufficiently small complexity costs, indirect invasions - but now through 'almost neutral' mutants - become an important ingredient of the dynamics. These indirect invasions include stepping stone paths out of full defection.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-089/I.

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Date of creation: 06 Sep 2012
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Handle: RePEc:dgr:uvatin:20120089

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Web page: http://www.tinbergen.nl

Related research

Keywords: repeated games; evolutionary game theory; complexity costs; indirect invasions; robustness against indirect invasions; neutrally stable strategy; evolutionarily stable strategy; iterated prisoners dilemma;

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  1. Matthijs van Veelen, 2007. "Evolution of Strategies in Repeated Games with Discounting," Tinbergen Institute Discussion Papers 06-115/1, Tinbergen Institute.
  2. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
  3. van Veelen, Matthijs, 2012. "Robustness against indirect invasions," Games and Economic Behavior, Elsevier, vol. 74(1), pages 382-393.
  4. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer, vol. 29(4), pages 571-595.
  5. Linster, Bruce G, 1994. "Stochastic Evolutionary Dynamics in the Repeated Prisoners' Dilemma," Economic Inquiry, Western Economic Association International, vol. 32(2), pages 342-57, April.
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