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

Tinbergen Institute Discussion Paper 12-089/I

33 Pages Posted: 7 Sep 2012

See all articles by Matthijs van Veelen

Matthijs van Veelen

University of Amsterdam - Amsterdam School of Economics (ASE); Tinbergen Institute

Julian Garcia

Max Planck Institute for Evolutionary Biology

Date Written: September 3, 2012

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.

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

JEL Classification: C73

Suggested Citation

van Veelen, Matthijs and Garcia, Julian, In and Out of Equilibrium II: Evolution in Repeated Games with Discounting and Complexity Costs (September 3, 2012). Tinbergen Institute Discussion Paper 12-089/I, Available at SSRN: https://ssrn.com/abstract=2142512 or http://dx.doi.org/10.2139/ssrn.2142512

Matthijs Van Veelen (Contact Author)

University of Amsterdam - Amsterdam School of Economics (ASE) ( email )

Roetersstraat 11
Amsterdam, North Holland 1018 WB
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Julian Garcia

Max Planck Institute for Evolutionary Biology ( email )

August-Thienemann-Str. 2
Plön, 24306
Germany

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