On Coalition Incentive Compatibility

Abstract

Progress has recently been made in the study of mechanisms designed to elicit, from economic agents, truthful revelation of their characteristics. The relevance of these results is best illustrated with reference to the free rider problem which occurs in public decision making. The Government must know agents' preferences to choose the best public projects, but it may be in agents' interest to provide distorted reports on their preferences. A class of mechanisms has been proposed by Vickrey (1961), Clarke (1971), Groves (1973) which has the property that, in environments with separable utility functions, truthful revelation of preferences is a dominant strategy for each individual and a Pareto optimal decision is taken. In this context, since unrestricted transfers of a private resource are allowed, Pareto optimality is interpreted to mean that the public decision taken is the same as that which would be associated with all Pareto optimal resource allocations. Alternatively, recognizing that the mechanism may engender a surplus or a deficit, it is natural to introduce an artificial agent (the government or planner) capable of absorbing this imbalance. Using the net transfer to this agent as his utility function, Pareto optimality can be interpreted in the usual manner for the enlarged set of agents. The impossibility of closing the mechanism while maintaining optimality and incentive compatibility has been proven by Hurwicz (1975), Green and Laffont (1976a) and Walker (1976) in various contexts. In Green and Laffont (1975) we have shown that the class of mechanisms proposed by Groves includes all such mechanisms. Furthermore, allowing more general mechanisms, we have proved that any satisfactory mechanism (i.e. any mechanism which takes Pareto optimal decisions and for which dominant strategies exist) is isomorphic to a Groves mechanism. The incentive compatibility obtained with these mechanisms applies to individuals; for each agent the truth is his best possible answer for any willingnesses to pay professed by the others. Even though it was soon realized (see Bennett and Conn (1976), Groves (1973) and Vickrey (1961)) that these mechanisms are vulnerable to manipulation by coalitions no analytical attempt to ameliorate this situation has yet been made. In Green and Laffont (1976b) we suggested the use of a sampling version of Groves mechanisms to mitigate this coalition problem by making cooperation very costly and unlikely. The purpose of this paper is to look more carefully into this question. If the structure of binding coalitions forms a partition of the agents and is known to the decision maker, then, by treating each coalition as a single agent, it is still possible to induce truthful revelation. When the decision maker does not know this structure, or when, a priori, any structure is possible, the mechanism must be designed to be incentive compatible for any coalition. This is clearly impossible. Should we then say that no positive result concerning coalition incentive compatibility can be obtained for Groves mechanisms?