Cooperation and distributed optimization for the unreliable wireless game with indirect reciprocity

Cooperation in packet forwarding among users and operators of a distributed wireless network has been widely studied. However, because of the limited computational resources, users in wireless communication do not prefer to cooperate with others unless cooperation may improve their own performance. Therefore, the key problem in cooperation enforcement must be solved first to enable a wireless network to be efficient. Yet, most of the existing game-theoretic cooperation stimulation approaches assume that the interactions between any pair of players (users) are long-lasting. In this paper, we apply game theory to optimize the communication efficiency of a distributed wireless network with finite number of interactions between any pair of players. Based on the mechanism of indirect reciprocity, we theoretically analyze the optimal action rule with the method of dynamic programming, and derive the approximate threshold of benefit-to-cost ratio to achieve the optimal action rule. Furthermore, we adopt the replicator dynamics to assess the evolutionary stability of the optimal action rule against the perturbation effect. Numerical illustrations verify the performance of the proposed method on wireless cooperation.