Prisoner's Dilemma Game on Complex Networks with Agents' Adaptive Expectations

In the spatial prisoner's dilemma game, an agent's strategy choice depends upon the strategies he expects his neighboring agents to adopt. Yet, the expectation of agents in the games has not been studied seriously by the researchers of games in complex networks. The present paper studies the effect of the agents' adaptive expectation on cooperation emergence in the prisoner's dilemma game in complex networks from an agent-based approach. Simulation results show that the agents' adaptive expectation will favor the emergence of cooperation. However, due to agents' adaptive behavior, agents' initial expectation level does not greatly affect the cooperation frequency in the experiments. Simulation results also show that the agents' expectation adjustment speed significantly affects the cooperation frequency. In addition, the initial number of cooperation agents on the network is not a critical factor in the simulations. However, together with a bigger defection temptation, a larger neighborhood size will produce greater cooperation frequency fluctuations in a Barabási and Albert (BA) network, a feature different from that of Watts and Strogatz (WS) small world networks, which can be explained by their different networks degree distributions. Simulation results show that the cooperation frequency oscillating on the WS network is much smaller than that of the BA networks when defection temptation becomes larger. This research demonstrates that agent's adaptive expectation plays an important role in cooperation emergence on complex networks and it deserves more attentions.