Potentials and Implementation Philippe Jehiel, Moritz Meyer-ter-Vehn and Benny Moldovanu ∗ September 1, 2004 Abstract We introduce the concept of potentials (formally analogous to Monderer and Shapley (1996)) for mechanism design problems with interdependent valuations, and relate potentials to implementation in ex-post equilibria. We go on to show that ordinal and cardinal poten- tial coincide in settings with separable valuation functions. 1 Introduction Aligning the interests of several heterogenous strategic agents that jointly control a decision is a central desideratum in mechanism design and im- plementation. By attaching different monetary transfers to different social alternatives, the designer can affect the agents’ preferences over these alter- natives so that, ultimately, all agents agree about the preferred alternative (and hence all agents find it in their own strategic interest to behave in a way that leads to the commonly preferred alternative). The most famous example of successful alignment is offered by the Vickrey- Clarke-Groves mechanisms (see Vickrey (1961), Clarke (1971) Groves (1973)) for private values environments with quasi-linear utility. There, an agent re- ceives a transfer equal to the sum of valuations of the other agents in the chosen social alternative. With such transfers all individual payoff maxi- mization decision problems coincide with the maximization of social surplus, yielding the well known dominant strategy implementability of the efficient choice rule. More generally, we say that a mechanism design problem with given val- uation functions admits a potential if there exist monetary transfers such ∗ Jehiel: UCL London and CERAS, Paris; jehiel@enpc.fr; Meyer-ter-Vehn and Moldovanu: University of Bonn; moritz mtv@web.de, mold@uni-bonn.de 1