I consider a strategic game form with a finite set of payoff states and employ undominated Nash equilibrium (UNE) as a solution concept under complete information. I propose notions of the proximity of information according to which the continuity of UNE concept is considered as the robustness criterion. I identify a topology (induced by what I call d?) with respect to which the undominated Bayesian Nash equilibrium (UBNE) correspondence associated with any game form is upper hemi-continuous at any complete information prior. I also identify a slightly coarser topology (induced by what I call d??) with respect to which the UBNE correspondence associated with some game form exhibits a failure of the upper hemi-continuity at any complete information prior. In this sense, the topology induced by d? is the coarsest one. The topology induced by d?? is also used in both Kajii and Morris (1998) and Monderer and Samet (1989, 1996) with some additional restriction. I apply this robustness analysis to the UNE implementation. Appealing to Palfrey and Srivastava’s (1991) canonical game form, I show, as a corollary, that almost any social choice function is robustly UNE implementable relative to d?. I show, on the other hand, that only monotonic social choice functions can be robustly UNE implementable relative to d??. This clarifies when Chung and Ely’s Theorem 1 2003) applies.
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Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number
2006-26.
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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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