Modeling territorial disputes with Hawk–Dove games

We investigate the evolutionary dynamics of territorial contests by extending the classical Hawk–Dove game to explicitly incorporate site exchange into the game’s payoff structure. In our model, individuals occupy sites on a square lattice, with a fixed fraction designated as high-value territories that confer fitness benefits. Territorial disputes are resolved through Hawk–Dove interactions, and site occupation changes accordingly. Our analysis shows that, although the average payoff matrix remains the same as in traditional models, coupling of payoff determination with site exchanges reduces the prevalence of non-aggressive strategies. We also examine how the spatial distribution of valuable sites affects outcomes, showing that structured patterns – such as chessboard-like arrangements – can sustain Doves under specific dynamic regimes. Furthermore, when both Hawks incur conflict costs, Doves can persist even in resource-rich environments. These findings highlight the importance of coupling mobility, spatial structure, and payoff mechanisms in understanding the evolution of conflict and cooperation in territorial systems.