Efficiency and redistribution in dynamic mechanism design

The emerging area of dynamic mechanism design seeks to achieve desirable equilibrium outcomes in multi-agent sequential decision-making problems with self-interest. Here we take the goal of maximizing social welfare. We start by extending the characterization result of Green & Laffont [1977] to a dynamic setting, defining the dynamic-Groves class of dynamic mechanisms and showing that it exactly corresponds to the set of mechanisms that are efficient (social welfare maximizing) and incentive compatible in an ex post equilibrium. The dynamic-VCG mechanism of Bergemann & Valimaki [2006] is a dynamic analogue of the static VCG mechanism and is efficient, incentive compatible, and individual rational in an ex post equilibrium; we use our characterization result to show here that it is also revenue maximizing among all dynamic mechanisms with these properties. In other words, dynamic-VCG maximizes the payments required of the agents and thus, while perhaps desirable for an auctioneer seeking high revenue, is in fact worst when maximizing agent utility is the goal. We then build on recent work on static redistribution mechanisms (see [Cavallo, 2006]) to design a dynamic redistribution mechanism for multi-armed bandit settings (e.g., the repeated allocation of a single good) that returns much of the revenue under dynamic-VCG back to the agents, while maintaining the same efficiency, incentive compatibility, individual rationality, and no-deficit properties. We conclude with a numerical analysis, demonstrating empirically that this redistribution mechanism typically comes close to perfect budget balance.