Incentive Mechanisms for Fairness Among Strategic Agents

Mechanism design for incentivizing strategic agents to maximize their sum of utilities (SoU) is a well-studied problem in the context of resource allocation in networks. There are, however, a number of network resource allocation problems of interest where a designer may have a different objective than maximization of the SoU. The obvious reason for seeking a different objective is that this notion of efficiency does not account for fairness of allocation. A second, more subtle, reason for demanding fairer allocation is that it indirectly implies less variation in taxes paid by agents. This is desirable in a situation where implicit individual agent budgetary constraints make payment of large taxes unrealistic. In this paper, we study a family of social utilities that provide fair allocation (with SoU being subsumed as an extreme case) and derive conditions under which Bayesian and dominant strategy implementation is possible. Furthermore, it is shown how a modification of the above-mentioned mechanism by adding just one message per agent can guarantee full Bayesian implementation, i.e., no extraneous equilibria. We consider the problem of demand-side management in smart grids as a specific motivating application, and through numerical analysis, it is demonstrated that in this application, the proposed method can result in significant gains in fairness of allocation and a reduction in tax variation among agents.