The Territorial Raider Game and Graph Derangements
Abstract
A derangement of a graph $G=(V,E)$ is an injective function $f:V\to V$ such that for all $v\in V$, $f(v)\neq v$ and $(v,f(v))\in E$. 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 $G$.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2015
- DOI:
- 10.48550/arXiv.1507.06286
- arXiv:
- arXiv:1507.06286
- Bibcode:
- 2015arXiv150706286G
- Keywords:
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- Mathematics - Combinatorics;
- 91A43;
- 05C75;
- 05C70;
- 91A06