A general framework for analysing multiplayer games in networks using territorial interactions as a case study

Recently, models of evolution have begun to incorporate structured populations, including spatial structure, through the modelling of evolutionary processes on graphs (evolutionary graph theory). One limitation of this otherwise quite general framework is that interactions are restricted to pairwise ones, through the edges connecting pairs of individuals. Yet, many animal interactions can involve many players, and theoretical models also describe such multiplayer interactions. We shall discuss a more general modelling framework of interactions of structured populations with the focus on competition between territorial animals, where each animal or animal group has a “home range” which overlaps with a number of others, and interactions between various group sizes are possible. Depending upon the behaviour concerned we can embed the results of different evolutionary games within our structure, as occurs for pairwise games such as the Prisoner's Dilemma or the Hawk–Dove game on graphs. We discuss some examples together with some important differences between this approach and evolutionary graph theory.

► We introduce a new general framework for interaction within structured populations.
► Unlike evolutionary graph theory, our framework allows multi-player interactions.
► We apply our framework to the case of animal territorial interactions.
► We show a natural way of evaluating individual fitness for games on graphs.
► We show how to compare structures with equivalent well-mixed populations fairly.