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

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  • 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.

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20120089
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    References listed on IDEAS

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    Cited by:

    1. Christopher Graser & Takako Fujiwara-Greve & Julian García & Matthijs van Veelen, 2024. "Repeated games with partner choice," Tinbergen Institute Discussion Papers 24-038/I, Tinbergen Institute.
    2. Christopher Graser & Matthijs van Veelen, 2024. "Repeated prisoner’s dilemmas with errors: how much subgame-perfection, how much forgiveness, and how much cooperation?," Tinbergen Institute Discussion Papers 24-022/I, Tinbergen Institute.
    3. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.

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    More about this item

    Keywords

    repeated games; evolutionary game theory; complexity costs; indirect invasions; robustness against indirect invasions; neutrally stable strategy; evolutionarily stable strategy; iterated prisoners dilemma;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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