Abstract: The evolution of cooperation in prisoner's dilemma game (PDG) and snow game (SG) on scale-free networks has been explored in this study. One-shot two-person game is played between neighbors on scale-free networks. Players have two possible strategies, cooperate or defect, and the strategies evolve according to the update rule of limited population analogue of replicator dynamics. Different from previous studies in which a player can interact with all his neighbors in every round of the game, this work proposes a new interaction pattern of players. A player can interact with at most W neighbors in every round of the game, who are named as interacting-neighbors. The value of W reflects the limited time and energy of players, and thus describes the limited interaction level of players in a networked PDG and SG. Results indicate that a high-level of cooperation in PDG and SG can be achieved on scale-free networks as long as high-connectivity players interact with a small fraction of their neighbors, and the interaction levels of players have significant positive effects on cooperation. These results suggest that even if individuals in real world have limited time and energy to interact with each other, they could still preserve cooperation because their interactions are rooted in actual scale-free networks. Moreover, high-connectivity individuals such as leaders or directors in an organization, who generally prefer interacting with each other in real world, play an important role in the evolution of cooperation. Current work provides a new interaction mechanism in networked game and contributes to understanding the emergence of cooperation in real society.

Key words: scale-free networks, prisoner's dilemma game, snowdrift game, cooperative behavior, game participation level