Predictors of Fixation Probability on Complete Networks Involving Multiplayer Interactions Under Coordinated Movement Systems

In recent years, classical evolutionary models have been extended to incorporate realistic multiplayer interactions rather than the traditional pairwise modelling approach. Several papers have introduced a new evolutionary framework involving population structure, evolutionary dynamics, multiplayer games and movement processes. The theory underlying the framework has been explored in several directions, identifying strong predictors of fixation probability, such as mean group size and temperature. A recent study developed an evolutionary model where individuals move in a coordinated manner via newly developed movement mechanisms, resulting in herding or separation within the population. This analysis demonstrated that these movement mechanisms impact the fixation probability of cooperation. This paper extends this analysis by investigating whether the previously identified predictors of fixation probability retain their strong influences under different games on complete graphs and by considering a different social dilemma in the form of the Stag-Hunt game. We show that previously defined measures of aggregation are directly related to mean group size and that these fundamental measures can be analytically calculated. In the Stag-Hunt game, we demonstrate that herding opposes the evolution of cooperation. In the Public Goods game, we demonstrate that temperature and fixation share a linear relationship regardless of the movement mechanism considered. In the Hawk-Dove game, temperature is a stronger predictor of fixation but the linear relationship breaks down for higher temperatures and a similar relationship holds as for the Stag-Hunt game.