Self-questioning dynamical evolutionary game in small-world networks

Self-questioning update rules is the selected process of the optimal strategy of the individuals by comparing the payoff from various alternative strategies. In this paper, a self-questioning dynamical evolutionary game with altruistic or spiteful preferences via weighted sums of own and opponent’s payoffs is studied. In order to obtain the influence of longrange connections and degree heterogeneity on evolutionary game model, we study three kinds of spatial structure: the two-dimensional lattice, homogeneous small-world networks (only the introduction of long-range connections) and heterogenous small-world networks (both long-range connections and degree heterogeneity). Through the Ising model theory and Monte Carlo simulation the following conclusions are obtained: long-range connections make the individuals perplex in strategic choice which is similar to the state of frustration in spin glass; the degree heterogeneity makes the different individual has the different field (the more neighbours, the larger of field); when the field is positive, long-range connections promote cooperation, but the heterogeneity of degree inhibits the production of cooperation.