Vol. 7, No. 2, 2014

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Analysing territorial models on graphs

Marie Bruni, Mark Broom and Jan Rychtář

Vol. 7 (2014), No. 2, 129–149

Evolutionary graph theory combines evolutionary games with population structure, induced by the graph. The games used are limited to pairwise games occurring on the edges of the graph. Multiplayer games can be important in biological modelling, however, and so recently a new framework for modelling games in structured populations allowing games with arbitrary numbers of players was introduced. In this paper we develop the model to investigate the effect of population structure on the level of aggression, as opposed to a well-mixed population for two specific types of graph, using a multiplayer hawk-dove game. We find that the graph structure can have a significant effect on the level of aggression, and that a key factor is the variability of the group sizes formed to play the games; the more variable the group size, the lower the level of aggression, in general.

structured populations, evolution, game theory, territory
Mathematical Subject Classification 2010
Primary: 91A22
Secondary: 05C57, 91A43, 92B05
Received: 8 June 2012
Revised: 23 October 2012
Accepted: 17 November 2012
Published: 16 November 2013

Communicated by Kenneth S. Berenhaut
Marie Bruni
UFR de Mathématique et d’Informatique
University of Strasbourg
7 rue René Descartes
67084 Strasbourg Cedex
Mark Broom
Department of Mathematical Science
City University London
Northampton Square
United Kingdom
Jan Rychtář
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC 27402
United States