Jehiel, P.; Meyer-ter-Vehn, M.; Moldovanu, B.; (2008) Ex-post implementation and preference aggregation via potentials. (ELSE Working Papers 297). ESRC Centre for Economic Learning and Social Evolution: London, UK.

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Abstract

We introduce several notions of potentials for mechanism design problems with interdependent values, and relate them to implementation in ex-post equilibrium. Whereas ex-post implementation is closely linked to the ordinal concept of best-alternative potentials, the celebrated Vickrey-Clarke-Groves mechanism corresponds to the stronger notion of a cardinal potential: agents agree not only on the best al- ternative, but also on the quantitative differences between all alternatives. We characterize all valuations that allow for cardinal potentials, and use this characterization for: 1) Identifying valuations for which ex-post implementation is possible; 2) Identifying classes of valuations for which all ex-post implementable choice rules correspond to cardinal potentials. The latter allows us to extend to interdependent valuations a result for dominant strategy implementation in private values settings, due to Roberts (1979).

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