Evolutionary game dynamics with non-uniform interaction rates

Christine Taylor, Martin A. Nowak

Research output: Contribution to journalArticle

53 Scopus citations

Abstract

The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extension leads to non-linear fitness functions. We show that a strict Nash equilibrium remains uninvadable for non-uniform interaction rates, but the conditions for evolutionary stability need to be modified. We analyze all games between two strategies. If the two strategies coexist or exclude each other, then the evolutionary dynamics do not change qualitatively, only the location of the equilibrium point changes. If, however, one strategy dominates the other in the classical setting, then the introduction of non-uniform interaction rates can lead to a pair of interior equilibria. For the Prisoner's Dilemma, non-uniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, non-uniform interaction rates change the equilibrium frequency of cooperators.

Original languageEnglish (US)
Pages (from-to)243-252
Number of pages10
JournalTheoretical Population Biology
Volume69
Issue number3
DOIs
StatePublished - May 2006

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics

Keywords

  • Evolutionary game dynamics
  • Evolutionary stability
  • Kin selection
  • Non-uniform interaction rates
  • Prisoner's Dilemma
  • Replicator dynamics
  • Snowdrift game

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