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

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