Intervention in power control games with selfish users

We study the power control problem in single-hop wireless ad hoc networks with selfish users. Without incentive schemes, selfish users tend to transmit at their maximum power levels, causing excessive interference to each other. In this paper, we study a class of incentive schemes based on intervention to induce selfish users to transmit at desired power levels. In a power control scenario, an intervention scheme can be implemented by introducing an intervention device that can monitor the power levels of users and then transmit power to cause interference to users if necessary. Focusing on first-order intervention rules based on individual transmit powers, we derive conditions on the intervention rates and the power budget to achieve a desired outcome as a (unique) Nash equilibrium with intervention and propose a dynamic adjustment process to guide users and the intervention device to the desired outcome. We also analyze the effect of using aggregate receive power instead of individual transmit powers. Our results show that intervention schemes can be designed to achieve any positive power profile while using interference from the intervention device only as a threat. Lastly, simulation results are presented to illustrate the performance improvement from using intervention schemes and the theoretical results.