Repeated Games With Intervention: Theory and Applications in Communications

In communication systems where users share common resources, users' selfish behavior usually results in suboptimal resource utilization. There have been extensive works that model communication systems with selfish users as one-shot games and propose incentive schemes to achieve Pareto optimal action profiles as non-cooperative equilibria. However, in many communication systems, due to strong negative externalities among users, the sets of feasible payoffs in one-shot games are nonconvex. Thus, it is possible to expand the set of feasible payoffs by having users choose convex combinations of different payoffs. In this paper, we propose a repeated game model generalized by intervention. First, we use repeated games to convexify the set of feasible payoffs in one-shot games. Second, we combine conventional repeated games with intervention, originally proposed for one-shot games, to achieve a larger set of equilibrium payoffs and loosen requirements for users' patience to achieve it. We study the problem of maximizing a welfare function defined on users' equilibrium payoffs, subject to minimum payoff guarantees. Given the optimal equilibrium payoff, we derive the minimum intervention capability required and design corresponding equilibrium strategies. The proposed generalized repeated game model applies to various communication systems, such as power control and flow control.