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

TOHMÉ, FERNANDO; AUDAY, MARCELO

Evanston, Illinois (USA)

Congreso; Games 2008: Third World Congress of Game Theory; 2008

Kellogg School, Northwestern University

The theory of Mechanism Design intends to find ways to implementsocial choice functions. That is, to characterize rules such that, for anyprofile of actual preferences, game solutions support the outcomes of thosefunctions. Maskin, in his seminal 1977 paper showed that game formsprovide a natural framework to analyze this problem.We focus here on game forms in which the strategies are declarations ofpreferences over the outcomes. These game forms are called direct mechanisms.On the space of this kind of game forms we postulate an operation,that given a direct mechanism provides other mechanisms (not necessarilya single one), by optimizing the preferences of the agents. Fixed pointsunder this operation are shown to make each preference profile a Nashequilibrium in the corresponding game. Furthermore, we show that, sincethose profiles are dominant strategy equilibria, our fixed points supportstrategy-proof functions.