Online markets require simple, and well-designed systems that work well even if users participate in multiple ones in parallel. Traditional mechanism design has considered mechanisms only in isolation, and the mechanisms it proposes tend to be complex and impractical. In contrast, players typically participate in various mechanisms that are run by different principals (e.g. different sellers on eBay or different ad-exchange platforms) and coordinating them to run a single combined mechanism is infeasible or impractical. Even the simple and elegant Vickrey auction loses some of its appeal when not in isolation: when the overall value of each player is a complex function of the outcomes of different Vickrey auctions, the global mechanism is no longer truthful.
We initiate the study of efficient mechanism design with guaranteed good properties even when players participate in multiple different mechanisms simultaneously or sequentially. We define the class of smooth mechanisms, related to smooth games defined by Roughgarden, that can be thought of as mechanisms that generate approximately market clearing prices. We show that smooth mechanisms result in high quality outcome in equilibrium both in the full information setting and in the Bayesian setting with uncertainty about participants, as well as in learning outcomes. Our main result is to show that such mechanisms compose well: smoothness locally at each mechanism implies efficiency globally.
Joint work with Eva Tardos