On arbitrarily long periodic orbits of evolutionary games on graphs

Jeremias Epperlein, Vladimír Švígler

Research output: Contribution to journalArticlepeer-review


A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters describing social-dilemma games. We construct graphs and corresponding initial conditions whose trajectories are periodic with an arbitrary minimal period length. We also examine a periodic behavior of evolutionary games on graphs with the underlying graph being an acyclic (tree) graph. Astonishingly, even this acyclic structure allows for arbitrary long periodic behavior.

Original languageEnglish
Pages (from-to)1895-1915
Number of pages21
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number5
StatePublished - 1 Jul 2018
Externally publishedYes


  • Deterministic imitation dynamics
  • Discrete dynamical systems
  • Evolutionary games on graphs
  • Game theory
  • Periodic orbit

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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