How robust is undominated Nash implementation? - KUNIMOTO, Takashi (Institutional Knowledge at Singapore Management University, 2010)
Palfrey and Srivastava (1991) show that almost any social choice correspondence(SCC) is implemented in undominated Nash equilibrium, a refinement of Nash equilibrium. By requiring solution concepts to have closed graph in the limit of complete information, Chung and Ely (2003) investigate the robustness of undominated Nash implementation. Their robustness test concludes that when preferences are strict (or more generally, hedonic), only monotonic SCCs can be implemented in the closure of the undominated Nash (equilibrium) correspondence. This paper re-examines this robustness test. I show that almost any SCC is implemented in the closure of the undominated Nash correspondence, provided that the planner is certain that there is “approximate” common knowledge. I also show that only monotonic SCCs can be implemented in the closure of the undominated Nash correspondence, provided that the planner is only nearly certain that there is approximate common knowledge. Therefore, this robustness test, on the one hand, generates new restrictions imposed on the set of implementable SCCs, and on the other hand, clarifies the extent to which the permissive implementation results are sustained.