On The Non-Robustness Of Nash Implementation

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On The Non-Robustness Of Nash Implementation

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Takashi Kunimoto ()

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Takashi Kunimoto

Abstract

I consider the implementation problem under complete information and employ Nash equilibrium as a solution concept. A socially desirable rule is given as a correspondence from the set of states to the set of outcomes. This social choice rule is said to be implementable in Nash equilibrium if there exists a mechanism such that all (pure strategy)Nash equilibrium outcomes are socially desirable. Maskin (1999) clarified the conditions on the social choice rules under which he was able to construct a general Nash implementing mechanism when there are at least three players. This paper identifies the minimal amount of incomplete information which prevents the Maskinian mechanism from being robustly implemented in Nash equilibrium. More precisely, with mild constrains on the social choice rules, one can construct a canonical perturbation of the complete information structure under which a sequence of Bayesian Nash equilibria of the Maskinian mechanism supports a non-Nash equilibrium outcome in the limit of the space of the original complete information structure. Therefore, there is a minimal sense in which the Maskinian mechanism is not robust to incomplete information. This non-robustness result is also extended to the environment with two players.

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Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2006-25.

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Length: 24 pages
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:mcl:mclwop:2006-25

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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