Are We There Yet? Mechanism Design Beyond Equilibrium

There are mechanism design problems for which an exclusive focus on equilibrium can be seriously misleading. If outcomes will be implemented whether or not an equilibrium has been achieved, then the desiderata by which we evaluate mechanisms in these situations need to include more than merely the properties of their equilibria (are the equilibria Pareto optimal; are they in dominant strategies; are they stable; etc.). For the classical public-goods problem, we describe some of our research in which (1) we showed, in an experiment, that several mechanisms with excellent equilibrium properties exhibited serious out-of-equilibrium failures; (2) by emulating the Walrasian exchange model, we designed a publicgood mechanism to be transparent and to have reasonable properties even when out of equilibrium; and (3) we conducted an experiment in which this new mechanism performed better than previous mechanisms. * [email protected] ‡ [email protected] In mechanism design, Leo Hurwicz created a new field of economics. He used the theory to bring informational and incentive issues to the fore, and to address two fundamental questions in economics: in classical allocation problems, what can economic institutions achieve, and what can’t they achieve? (Hurwicz 1979, 1990). The tool he used, and the one we’ve all used ever since, is game theoretic equilibrium. The two classical allocation problems that Leo addressed were price formation in the pure exchange problem and the “free rider problem” with public goods. In both problems it’s noteworthy that we often implement outcomes in real time, as our institutions produce them, rather than waiting to attain an equilibrium and asking along the way “Are we there yet?” Realistically, we are probably never really at an equilibrium. Equilibrium predictions are useful when we think we will at least be “close to” an equilibrium, reasonably quickly, or when our interest is primarily in a system’s long-run state. But if outcomes are going to be implemented in or out of equilibrium, then clearly we need to know something about disequilibrium outcomes. Knowing only about equilibrium outcomes is not good enough. We view this as a variation on Wilson’s argument for “robust” mechanism design (Wilson 1987). Wilson’s emphasis was on the theory’s assumption of common knowledge of the participants’ preferences and information. Milgrom subsequently went further, maintaining that “the behavior of [a mechanism’s participants] cannot be regarded as perfectly predictable” (Milgrom 2004). Milgrom’s larger point was that when mechanism design is required to actually perform well on the ground, “mechanisms that are optimized to perform well when the assumptions are exactly true may still fail miserably in the much more frequent cases when the assumptions are untrue.” We take this view a step further, treating the idea that the players in a game will play equilibrium strategies as an additional assumption. In some cases the equilibrium assumption is fruitful: the equilibrium prediction is close enough to the choices the players actually make, and this tells us with some degree of accuracy what the welfare implications will be and what will happen if we change the rules of the game or if some features of the environment change. But this requires either that we determine, for any given mechanism, whether actual participants will play “close enough” to equilibrium, or else that we design the mechanism in the first place to be “robust” to non-equilibrium play.