Max-min Fairness of Generalized AGV Mechanisms

We generalize the standard Arrow-d'Aspremont-Gerard-Varet (AGV) mechanism to balance the (ex-ante) net payoffs received by all agents, while maintaining Bayesian incentive compatibility, ex-post efficiency, and ex-post budget balance of the standard AGV mechanism. In a private-value environment with independent agents' types and the principal's cost, we show (under mild conditions) the existence of a generalized AGV mechanism that yields all agents the same ex-ante payoff. Since a generalized AGV mechanism is designed to be ex-post budget balanced, equal distribution of ex-ante social welfare immediately guarantees ex-ante individual rationality (for all agents), as long as the ex-ante social welfare is nonnegative. To mitigate the volatility of agents' ex-post payoffs, we formulate the problem of ex-post payoff variance minimization (subject to equal distribution of ex-ante net benefit) as a biconvex program. We propose an effective heuristic algorithm to solve this (non-convex) optimization problem. Finally, we apply the constructed theoretic framework to a case study on market design for energy management in shared spaces.