Repeated Games with Intervention: Theory and Applications in Communications

Abstract

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.

Cooperative Overlay Spectrum Access in Cognitive Radio Networks

“…Zhou et al [99] Reinforcement Learning for Repeated Power Control Game in Cognitive Radio Networks. Xiao et al [100] By using intervention in repeated games we can achieve a larger set of equilibrium payoffs and loosen requirements for users' patience to achieve a target payoff. Hamouda et al [101] A cooperative physical resource blocks (PRBs) sharing scheme in a dual-hop LTE-Advanced in which every node can transmit on some of the PRBs assigned to a coexisting node without causing it harmful interference.…”

Applications of Repeated Games in Wireless Networks: A Survey

“…In [128], the authors used an intervention scheme [129] for repeated games with the aim to enlarge the limit set of equilibrium payoffs and loosen the conditions for the discount factor that needs to be close to one in general repeated games. In the intervention scheme, an intervention device is introduced to observe and intervene interactions among SUs.…”

Distributed spectrum sharing policies for selfish users with imperfect monitoring ability

“…4, we compare the average throughput of the pro posed policy with that of existing policies with time-varying power levels [10]- [13]. Specifically, we consider the "punish forgive" policy in [10]- [13], which requires SUs to switch to the punishment phase once a deviation is detected. In the punishment phase, all the SUs transmit at the maximum power levels.…”

“…Hence, the spectrum sharing policy should be deviation-proof, such that selfish SUs cannot improve their QoS by deviating from the policy.Deviation-proof spectrum sharing policies with time varying power levels were studied in[10]-[13], under the assumption of peifect monitoring, namely the assumption that each SU can perfectly monitor the individual transmit power levels of all the other SUs. In the policies in [10]-[13], when a deviation from the prescribed policy by any user is detected, a punishment phase will be triggered. In the punishment phase, all the users transmit at the maximum power levels to create strong interference to each other, resulting in low QoS of all the users as a punishment.…”

“…Thus, the users' average payoffs cannot be Pareto optimal because of the low payoffs received in the punishment phases. Hence, the policies in [10]-[13] must have performance loss in practice where the monitoring is always imperfect.…”