Transition matrix model for evolutionary game dynamics

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

Evolutionary Game
Transition Model
Transition Matrix
Matrix Models
games
Folk Theorem
mutations
Limit Cycle
Hopf Bifurcation
preserving
proportion
Mutation
Proportion
theorems
Strategy
Model
rocks
Game
Model-based
cycles

All Science Journal Classification (ASJC) codes

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

Cite this

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Transition matrix model for evolutionary game dynamics. / Ermentrout, G. Bard; Griffin, Christopher; Belmonte, Andrew.

In: Physical Review E, Vol. 93, No. 3, 032138, 21.03.2016.

Research output: Contribution to journalArticle

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