On arbitrarily long periodic orbits of evolutionary games on graphs

Jeremias Epperlein; Vladimír Švígler

doi:10.3934/dcdsb.2018187

On arbitrarily long periodic orbits of evolutionary games on graphs

Jeremias Epperlein, Vladimír Švígler

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1895-1915
Number of pages	21
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	23
Issue number	5
DOIs	https://doi.org/10.3934/dcdsb.2018187
State	Published - 1 Jul 2018
Externally published	Yes

Keywords

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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10.3934/dcdsb.2018187

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AB - 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.

KW - Deterministic imitation dynamics

KW - Discrete dynamical systems

KW - Evolutionary games on graphs

KW - Game theory

KW - Periodic orbit

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On arbitrarily long periodic orbits of evolutionary games on graphs

Abstract

Keywords

ASJC Scopus subject areas

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