Repeated Game Analysis for Cooperative MAC With Incentive Design for Wireless Networks

Abstract

Cooperative communications offer appealing potentials to improve quality of service (QoS) for wireless networks. Many existing works on cooperative communications assume that participation in cooperative relaying is unconditional. In practice, however, due to resource consumption, it is vital to provide incentives for selfish cooperating peer nodes. In this paper, we analyze a cooperative medium access control (MAC) protocol with incentive design using a game-theoretic approach. Specifically, our analysis addresses two questions: 1) Can a cooperating agreement be reached between peer nodes, and 2) can cooperating lead to higher utility than not cooperating? We first formulate a one-stage game for the slotted-Aloha-based cooperative MAC protocol, where not cooperating is a Nash equilibrium (NE) strategy, whereas cooperating is not. To exploit cooperation gain, the one-stage game is extended to a two-stage game by incorporating an incentive mechanism that adapts channel access probabilities with tuning factors. Based on the Markov chain analysis of the system states with the repeated two-stage games, we determine valid tuning factors, guaranteeing that cooperating attains an NE and provides expected utility not less than that of the not-cooperating NE. Moreover, a special case with saturated and symmetric assumptions is investigated, and closed-form criteria for the tuning factors are derived. Finally, we compare the derived tuning factors for individual nodes with an optimal choice that is selected from the system perspective to maximize the overall system utility. The numerical results confirm our analytical conclusions and demonstrate that the tuning factors selected according to our derived criteria can achieve high utility that is slightly lower than that of the optimal choice.