Abstract
This paper proposes a novel system design for wireless relay networks formed of self-interested users that relies on token exchanges. Our emphasis in this paper is on developing optimal designs for token systems to be deployed in relay networks. The optimal designs aim to maximize the probability that the relay transmission will be executed by transceivers whenever they are requested to provide such services. We prove that the efficiency of the relay network heavily depends on issuing the optimal amount of tokens rather than an arbitrary amount. We formulate the design problem of the token system as a bi-level optimization problem. In the inner level optimization problem, we determine the transceivers' incentive-compatible strategies (i.e. the strategies that maximize the transceivers' own utilities). We prove that these strategies exhibit a simple threshold structure. The outer level problem determines the optimal token amount, which maximizes the overall relay network efficiency. We prove that the optimal amount of tokens tokens needs to be neither too small nor too large and depends on the threshold that the self-interested transceivers adopt in the inner level problem.