Dynamics of multiplayer games on complex networks using territorial interactions

The modelling of evolution in structured populations has been significantly advanced by evolutionary graph theory, which incorporates pairwise relationships between individuals on a network. More recently, a new framework has been developed to allow for multi-player interactions of variable size in more flexible and potentially changing population structures. While the theory within this framework has been developed, and simple structures considered, there has been no systematic consideration of a large range of different population structures, which is the subject of this paper. We consider a large range of underlying graphical structures for the territorial raider model, the most commonly used model in the new structure, and consider a variety of important properties of our structures with the aim of finding factors that determine the fixation probability of mutants. We find that the graphical temperature and the average group size, as previously defined, are strong predictors of fixation probability, whilst all other properties considered are poor predictors, although the clustering coefficient is a useful secondary predictor when combined with either of temperature or group size. The relationship between temperature/average group size and fixation probability is sometimes, however, non-monotonic, with a directional reverse occurring around the temperature associated with what we term “completely mixed” populations in the case of the Hawk-Dove game, but not the Public Goods game.