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 opponents payoffs is studied. In order to obtain the influence of long-range 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.