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Título: The Robustness of equilibrium analysis: the case of undominated Nash equilibrium
Autores: Kunimoto, Takashi
Fecha: 2006
2006-12-20
Publicador: McGill University - MCGILL
Fuente:
Tipo: Text
Tema: Approximate common knowledge
Implementation
Undominated Nash equilibrium
Descripción: 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.
Idioma: eng