A new characterization of the Groves-Clarke mechanism (Q1189330)

Suppose a group of individuals must choose a public project from some feasible set. If preferences are quasi-linear, the so-called Groves mechanism [\textit{T. Groves}, Econometrica 41, 617-631 (1973; Zbl 0311.90002)] induces truthful revelation of preferences and recommends projects that maximize the sum of the individual valuations. Unfortunately, there is not much freedom to achieve distributional objectives within the class of Groves mechanisms [see \textit{J. R. Green} and \textit{J.-J. Laffont}, ``Incentives in public decision-making'' (1979; Zbl 0417.90001), ch. 4]. Nevertheless, there is a sense in which one particular Groves mechanism, the Groves-Clarke (pivotal) mechanism, is equitable: It taxes individuals according to the cost they impose on others. A closely related notion is the Shapley value, which rewards a player according to his contribution to the `worth' of each coalition. This note characterizes the Groves-Clarke mechanism as the Groves mechanism whose payoff vector is the Shapley value of a certain cooperative game with transferable utility. In this game, it is assumed that each coalition would operate some Groves mechanism if they had to choose a project on their own. The proof uses the remarkable potential approach due to \textit{S. Hart} and \textit{A. Mas-Colell} [in: The Shapley value. Essays in Honor of Lloyd S. Shapley, 127-137 (1989; Zbl 0708.90099)]. Earlier characterizations of the Groves-Clarke mechanism can be found in a paper of \textit{H. Moulin} [J. Publ. Econ. 31, 53-78 (1986)]. It may be noted that, in a private goods context the Vickrey auction can be characterized in a similar way. However, the Vickrey auction generates a deficit which would make it necessary to subsidize coalitions.