Title: NASH IMPLEMENTATION USING SIMPLE MECHANISMS WITHOUT UNDESIRABLE MIXED-STRATEGY EQUILIBRIA
Abstract:This note shows that, in separable environments, any monotonic social choice function can be Nash implemented with a mechanism that makes no use of integer games or similar constructions and admits no...This note shows that, in separable environments, any monotonic social choice function can be Nash implemented with a mechanism that makes no use of integer games or similar constructions and admits no mixed-strategy Nash equilibria in undominated strate- gies that lead to undesirable outcomes with positive probability. Implementation theory studies the problem of designing a mechanism such that all its equi- libria yield outcomes coinciding with the value of a given social choice correspondence. In a seminal paper, Maskin (1999) provides a necessary and almost sucient condition (mono- tonicity) for a social choice correspondence to be implementable in Nash equilibrium. The suciency proof is by construction, and the constructed mechanism makes use of an integer game, whereby each player has to name an integer, and the one who names the highest integer gets to choose the allocation to be implemented. The integer game is helpful in eliminat- ing undesired equilibria, but the best-response correspondences are not well-dened in this game, so it is not clear how a participant should act in response to certain strategies of his opponents. Saijo (1988) proposes an alternative proof of Maskin's result, which replaces the integer game with a modulo game. The modulo game involves each agent naming an integer from a bounded set; the agent whose index equals the sum of the named integers modulo the number of agents gets to choose the allocation. The modulo game does not require an innite strategy space, but can possess mixed-strategy equilibria that can result in undesiredRead More
Publication Year: 2011
Publication Date: 2011-01-01
Language: en
Type: article
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Cited By Count: 3
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