arXiv:1805.03849 Abstract | arXiv Analytics

arXiv:1805.03849 [math.DS]Abstract References Reviews Resources

On Arbitrarily Long Periodic Orbits of Evolutionary Games on Graphs

Published 2018-05-10Version 1

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.

Categories: math.DS, math.CO

Subjects: 91A22, 05C57, 91A43, 37N40

Keywords: arbitrarily long periodic orbits, evolutionary games, arbitrary long periodic behavior, arbitrary minimal period length, display periodic behavior

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