Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics

Jeremias  Epperlein; Stefan  Siegmund; Petr  Stehlík; Vladimír  Švígler

doi:10.3934/dcdsb.2016.21.803

Article Contents

2016, Volume 21, Issue 3: 803-813. Doi: 10.3934/dcdsb.2016.21.803

This issue Previous Article Global well-posedness for a fourth order pseudo-parabolic equation with memory and source terms Next Article On existence of wavefront solutions in mixed monotone reaction-diffusion systems

Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics

1.
Center for Dynamics & Institute for Analysis, Dept. of Mathematics, Technische Universitat Dresden, 01062, Dresden
2.
Dept. of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitni 8, 30614 Pilsen, Pilsen

Received: June 30, 2015

Revised: October 31, 2015

Published: April 2016

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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.

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Mathematics Subject Classification: 05C90, 37N25, 37N40, 91A22.

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