Paid Access to Information Promotes the Emergence of Cooperation in the Spatial Prisoner's Dilemma

In biological evolution, organisms that are more adapted to the environment tend to survive better, which can be explained in part by evolutionary game theory. In this paper, we propose an improved spatial prisoner's dilemma game model, which allows the focal player to access the strategy of other agents beyond their nearest neighbors with a specified probability. During the strategy update, a focal player usually picks up a randomly chosen neighbor according to a Fermi-like rule. However, in our model, unlike the traditional strategy imitation, a focal agent will decide to update their strategy through the modified rule with a specific probability q. In this case, the focal agent accesses n other individuals who have the same strategy as the imitated neighbor, where the information accessing cost needs to be paid, and then compares their discounted payoff with the average payoff of those n + 1 agents to make the decision of strategy adoption; otherwise, they only refer to their own payoff and their neighbor's payoff to decide whether the strategy spread happens. Numerical simulations indicate that a moderate value of n can foster the evolution of cooperation very well, and increase in q will also improve the dilemma of cooperators. In addition, there exists an optimal product of n x c to cause the emergence of cooperation under the specific simulation setup. Taken together, the current results are conducive to understanding the evolution of cooperation within a structured population.