The Territorial Raider game and graph derangements

A derangement of a graph G=(V,E) is an injective function f:V→V such that for all v∈V, f(v)≠v and (v,f(v))∈E. Not all graphs admit a derangement and previous results have characterized graphs with derangements using neighborhood conditions for subsets of V. We establish an alternative criterion for...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 213; pp. 13 - 16
Main Authors Galanter, Nina, Silva, Dennis, Rowell, Jonathan T., Rychtář, Jan
Format Journal Article
LanguageEnglish
Published Elsevier B.V 20.11.2016
Subjects
Derangement
Game theory
Nash equilibrium
Nash equilibrium
Derangement
Game theory
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Summary:A derangement of a graph G=(V,E) is an injective function f:V→V such that for all v∈V, f(v)≠v and (v,f(v))∈E. Not all graphs admit a derangement and previous results have characterized graphs with derangements using neighborhood conditions for subsets of V. We establish an alternative criterion for the existence of derangements on a graph. We analyze strict Nash equilibria of the biologically motivated Territorial Raider game, a multi-player competition for resources in a spatially structured population based on animal raiding and defending behavior. We find that a graph G admits a derangement if and only if there is a strict Nash equilibrium of the Territorial Raider game on G.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2016.03.016