Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics

Jeremias Epperlein, Stefan Siegmund, Petr Stehlik, Vladimir Svigler

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Cooperative behaviour is often accompanied by the incentives to defect, i.e., to reap the benefits of others' efforts without own contribution. We provide evidence that cooperation and defection can coexist under very broad conditions in the framework of evolutionary games on graphs under deterministic imitation dynamics. Namely, we show that for all graphs there exist coexistence equilibria for certain game-theoretical parameters. Similarly, for all relevant game-theoretical parameters there exists a graph yielding coexistence equilibria. Our proofs are constructive and robust with respect to various utility functions which can be considered. Finally, we briefly discuss bounds for the number of coexistence equilibria.

Original languageEnglish
Pages (from-to)803-813
Number of pages11
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume21
Issue number3
DOIs
StatePublished - 1 May 2016
Externally publishedYes

Keywords

  • Coexistence
  • Cooperation
  • Equilibrium
  • Evolutionary games on graphs
  • Game theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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