Evolutionary games on graphs and discrete dynamical systems

Jeremias Epperlein, Stefan Siegmund, Petr Stehlík

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of attractor, update rules and update orders. We prove results on attractors for different utility functions and update orders. For complete graphs we characterize attractors for synchronous and sequential update rules. In other cases (for (Formula presented.) -regular graphs or for different update orders) we provide sufficient conditions for attractivity of full cooperation and full defection. We construct examples to show that these conditions are not necessary. Finally, by formulating a list of open questions we emphasize the advantages of our rigorous approach.

Original languageEnglish
Pages (from-to)72-95
Number of pages24
JournalJournal of Difference Equations and Applications
Issue number2
StatePublished - 1 Feb 2015
Externally publishedYes


  • attractors
  • cooperation
  • cycles
  • defection
  • discrete dynamical systems
  • evolutionary games on graphs
  • game theory
  • non-autonomous dynamical systems

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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