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In and Out of Equilibrium: Evolution of Strategies in Repeated Games with Discounting

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  • Matthijs van Veelen

    (CREED, Universiteit van Amsterdam)

  • Julian Garcia

    (Vrije Universiteit)

Abstract

Repeated games tend to have large sets 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 shows that for all of these neutrally stable strategies there is a stepping stone path out; there is always a neutral mutant that can enter a population and create an actual selective advantage for a second mutant. Such stepping stone paths out of equilibrium generally exist both in the direction of more and in the direction of less cooperation. While the central theorems show that such paths out of equilibrium exist, they could still be rare compared to the size of the strategy space. Simulations however suggest that they are not too rare to be found by a reasonable mutation process, and that typical simulation paths take the population from equilibrium to equilibrium through a series of indirect invasions. Instability does not mean we cannot draw qualitative conclusions though. The very nature of the indirect invasions implies that the population will on average be (somewhat) reciprocal and (reasonably) cooperative.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-037/1.

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Date of creation: 08 Apr 2010
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Handle: RePEc:dgr:uvatin:20100037

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

Related research

Keywords: Repeated games; evolution; robust against indirect invasions; simulation;

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  1. Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers, Tinbergen Institute 10-033/1, Tinbergen Institute.
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