Palfrey and Srivastava (1991) show that almost any social choice correspondence(SCC) is implemented in undominated Nash equilibrium, a refinement of Nash equilibrium. Byrequiring solution concepts to have closed graph in the limit of complete information, Chung andEly (2003) investigate the robustness of undominated Nash implementation. Their robustnesstest concludes that when preferences are strict (or more generally, hedonic), only monotonic SCCscan 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 implementedin the closure of the undominated Nash correspondence, provided that the planner is certainthat there is “approximate” common knowledge. I also show that only monotonic SCCs can beimplemented in the closure of the undominated Nash correspondence, provided that the planneris only nearly certain that there is approximate common knowledge. Therefore, this robustnesstest, 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 aresustained.
Approximate common knowledge, Implementation, Monotonicity, Robustness, Undominated Nash equilibrium
How robust is undominated nash implementation?. (2010). 1-30. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/2076
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.