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Implementation with Near‐Complete Information
Author(s) -
Chung KimSau,
Ely Jeffrey C.
Publication year - 2003
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00428
Subject(s) - social choice theory , mathematical economics , nash equilibrium , outcome (game theory) , social planner , monotonic function , planner , graph , best response , computer science , epsilon equilibrium , complete information , set (abstract data type) , mechanism design , mathematical optimization , solution concept , function (biology) , mathematics , economics , microeconomics , theoretical computer science , artificial intelligence , mathematical analysis , programming language , evolutionary biology , biology
Many refinements of Nash equilibrium yield solution correspondences that do not have closed graph in the space of payoffs or information. This has significance for implementation theory, especially under complete information. If a planner is concerned that all equilibria of his mechanism yield a desired outcome, and entertains the possibility that players may have even the slightest uncertainty about payoffs, then the planner should insist on a solution concept with closed graph. We show that this requirement entails substantial restrictions on the set of implementable social choice rules. In particular, when preferences are strict (or more generally, hedonic), while almost any social choice function can be implemented in undominated Nash equilibrium, only monotonic social choice functions can be implemented in the closure of the undominated Nash correspondence.