Spatial structure enhanced cooperation in dissatisfied adaptive snowdrift game

Abstract

The dissatisfied adaptive snowdrift game (DASG) describes the adaptive actions driven by the level of dissatisfaction when two connected agents interact. We study the DASG in static networks both numerically and analytically. In a random network of uniform degree k, the system evolves into a homogeneous state consisting only of cooperators when the cost-to-benefit ratio r < r ₀ and a mixed phase with the coexistence of cooperators and defectors when r > r ₀, where r ₀ is a threshold. For an infinite population, the large k limit corresponding to the well-mixed case is solved analytically. A theory is developed based on the pair approximation. It gives the frequency of cooperation f _c and the densities of different pairs that are in good agreement with simulation results. The results revealed that f _c is enhanced in networked populations with a finite k, when compared with the well-mixed case. The reasons that the theory works well for the present model are traced back to the weak spatial correlation implied by the random network and the fact that the adaptive actions in DASG are driven only by the strategy pairs. The results shed light on the class of models that the pair approximation is applicable.