title: A study of the dynamics of multi-player games on small networks using territorial interactions.
abstract: Recently, the study of structured populations using models of evolutionary processes on graphs has begun to incorporate a more general type of interaction between individuals, allowing multi-player games to be played among the population. In this paper, we develop a birth-death dynamics for use in such models and consider the evolution of populations for special cases of very small graphs where we can easily identify all of the population states and carry out exact analyses. To do so, we study two multi-player games, a Hawk-Dove game and a public goods game. Our focus is on finding the fixation probability of an individual from one type, cooperator or defector in the case of the public goods game, within a population of the other type. We compare this value for both games on several graphs under different parameter values and assumptions, and identify some interesting general features of our model. In particular there is a very close relationship between the fixation probability and the mean temperature, with high temperatures helping fitter individuals and punishing unfit ones and so enhancing selection, whereas low temperatures give a levelling effect which suppresses selection.
authors.affiliation: Department of Mathematics, City University London, Northampton Square, London, EC1V 0HB, UK. Mark.Broom@city.ac.uk.
authors.forename: Mark
authors.initials: M
authors.lastname: Broom
authors.affiliation: École Centrale Paris, Grande Voie des Vignes, 92 290, Châtenay-Malabry, France. charlotte.lafaye@student.ecp.fr.
authors.forename: Charlotte
authors.initials: C
authors.lastname: Lafaye
authors.affiliation: Department of Mathematics, City University London, Northampton Square, London, EC1V 0HB, UK. Karan.Pattni.1@city.ac.uk.
authors.forename: Karan
authors.initials: K
authors.lastname: Pattni
authors.affiliation: Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC, 27412, USA. rychtar@uncg.edu.
authors.forename: Jan
authors.initials: J
authors.lastname: Rychtář
mesh_terms: D000818:Animals; D005075:Biological Evolution; D005716:Game Theory; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D013731:Territoriality
keywords: Evolution; Evolutionary graph theory; Game theory; Structured populations; Territory