Discovering the effect of nonlocal payoff calculation on the stabilty of ESS: Spatial patterns of Hawk–Dove game in metapopulations

Abstract

The classical idea of evolutionarily stable strategy (ESS) modeling animal behavior does not involve any spatial dependence. We considered a spatial Hawk-Dove game played by animals in a patchy environment with wrap around boundaries. We posit that each site contains the same number of individuals. An evolution equation for analyzing the stability of the ESS is found as the mean dynamics of the classical frequency dependent Moran process coupled via migration and nonlocal payoff calculation in 1D and 2D habitats. The linear stability analysis of the model is performed and conditions to observe spatial patterns are investigated. For the nearest neighbor interactions (including von Neumann and Moore neighborhoods in 2D) we concluded that it is possible to destabilize the ESS of the game and observe pattern formation when the dispersal rate is small enough. We numerically investigate the spatial patterns arising from the replicator equations coupled via nearest neighbor payoff calculation and dispersal.

Analysis of stationary patterns arising from a time-discrete metapopulation model with nonlocal competition

“…Hence, we conclude that the smaller dispersal rate favors aggregation. This result is in line with the findings presented in [2,3,7,18] Instead of assuming nearest-neighbor interactions, we assumed that the strength of the ecological interactions (including dispersal) impinging on a population in a patch is a function of the neighboring population densities as well as of their spatial distance, with more distant patches having a smaller impact. Assuming nonlocal rather than quasi-local interactions leads to the emergence of more complex spatial patterns as shown in Figure 4.…”

“…This statement for more general nonlocal interactions takes the following mathematical form: if the DFS of the interaction kernel C k is negative for some k ∈ S then the spatially uniform equilibrium is unstable in the absence of dispersal. Note that the latter statement is known to hold for many other models taking nonlocal interactions into account (see, e.g., [2,3,4,5,18]).…”

Memory retrieval and harshness of conflict in the hawk–dove game

“…Consequently, the impact of an information advantage matters in a non-trivial way (Alós-Ferrer and Shi 2012), and our results indicate that it is an essential component that needs to be carefully considered when modelling the dynamics of conflict (Rusch and Gavrilets 2020). Since we obtain conditions under random matching of the members of two populations, future research should investigate the robustness of our results if mixing is assortative, interactions occur on social networks or if agents are spatially segregated (Aydogmus 2018).…”

On Equivalence of State Based Potential Games

“…Game theory was pioneered by John von Neumann to study the behavior in economic society 1 . Then, it has been developed rapidly and applied widely in various communities, including biology 2,3 , economics 4 , and engineering 5,6 . The concept of potential games was first put forward by Rosenthal 7 , which is called "congestion games".…”