Fixed Points of Choice-Improving Correspondences on the Space of Direct Mechanisms and Implementability

FERNANDO TOHMÉ; LEANDRO AROZAMENA; MARCELO AUDAY

San Luis

Workshop; Cooperation, Matching and Collective Goods; 2011

Association for Public Economic Theory y CONICET

The theory of Mechanism Design intends to find ways to implement social choice functions. That is, to characterize rules such that, for any profile of actual preferences, game solutions support the outcomes of those functions. Maskin, in his seminal 1977 paper, showed that {\em game forms} provide a natural framework to analyze this problem.We focus here on game forms in which the strategies are declarations of preferences over outcomes. These game forms are called {\it direct mechanisms}. On the space of this kind of game forms we postulate an operation that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. In complete information environments the fixed points under this operation are shown to make each preference profile a Nash equilibrium in the corresponding game. Furthermore, we show that, since those profiles are dominant strategy equilibria, our fixed points support {\em strategy-proof} functions. In the case of incomplete information with private values, we show that fixed points of the correspondence among direct mechanisms satisfy both {\em ex-post} incentive compatibility and {\em ex-post} monotonicity.