Dynamic Evolution with Limited Learning Information on a Small-World Network

This paper investigates the dynamic evolution with limited learning information on a small-world network.In the system, the information among the interaction players is not very lucid, and the players are not allowed to inspectthe profit collected by its neighbors, thus the focal player cannot choose randomly a neighbor or the wealthiest one andcompare its payoff to copy its strategy.It is assumed that the information acquainted by the player declines in theform of the exponential with the geographical distance between the players, and a parameter V is introduced to denotethe inspect-ability about the players.It is found that under the hospitable conditions, cooperation increases with therandomness and is inhibited by the large connectivity for the prisoner's dilemma; however, cooperation is maximal atthe moderate rewiring probability and is chaos with the connectivity for the snowdrift game.For the two games, theacuminous sight is in favor of the cooperation under the hospitable conditions; whereas, the myopic eyes are advantageousto cooperation and cooperation increases with the randomness under the hostile condition.