Nash Social Welfare Approximation for Strategic Agents

Abstract

We study the problem of allocating divisible resources to agents with different preferences. We analyze a market game known as Trading Post, first considered by Shapley and Shubik, where each agent gets a budget of virtual currency to bid on goods: after bids are placed, goods are allocated to players in proportion to their bids. In this setting, the agents choose their bids strategically, aiming to maximize their utility, and this gives rise to a game. We study the equilibrium allocations of this game, measuring the quality of an allocation via the Nash social welfare, the geometric mean of utilities (a measure of aggregate welfare that respects individual needs). We show that any Nash equilibrium of Trading Post approximates the optimal Nash welfare within a factor of two for all concave valuations, and the mechanism is essentially optimal for Leontief valuations.