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In and out of equilibrium II: Evolution in repeated games with discounting and complexity costs

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  • van Veelen, Matthijs
  • García, Julián

Abstract

We explore evolutionary dynamics for repeated games with small, but positive complexity costs. We begin by extending a folk theorem result by Cooper (1996) to continuation probabilities, or discount rates, smaller than 1. Then we show that All D has a uniform invasion barrier. Since none of the more cooperative equilibria are robust against indirect invasions, we might expect not to observe any cooperative equilibria when complexity costs are positive. The average level of cooperation in the dynamics, however, can hover anywhere between no cooperation at all, and the average level of cooperation in the absence of complexity costs, depending on how small complexity costs are and how large the population is.

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  • van Veelen, Matthijs & García, Julián, 2019. "In and out of equilibrium II: Evolution in repeated games with discounting and complexity costs," Games and Economic Behavior, Elsevier, vol. 115(C), pages 113-130.
    • Handle: RePEc:eee:gamebe:v:115:y:2019:i:c:p:113-130
    DOI: 10.1016/j.geb.2019.02.013
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    1. 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; Complexity costs; Neutrally stable strategy; Robust against indirect invasions; Uniform invasion barrier; Wright-Fisher process;
    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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