Transition matrix model for evolutionary game dynamics

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Abstract

We study an evolutionary game model based on a transition matrix approach, in which the total change in the proportion of a population playing a given strategy is summed directly over contributions from all other strategies. This general approach combines aspects of the traditional replicator model, such as preserving unpopulated strategies, with mutation-type dynamics, which allow for nonzero switching to unpopulated strategies, in terms of a single transition function. Under certain conditions, this model yields an endemic population playing non-Nash-equilibrium strategies. In addition, a Hopf bifurcation with a limit cycle may occur in the generalized rock-scissors-paper game, unlike the replicator equation. Nonetheless, many of the Folk Theorem results are shown to hold for this model.

Original languageEnglish (US)
Article number032138
JournalPhysical Review E
Volume93
Issue number3
DOIs
StatePublished - Mar 21 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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