Implementation with Near-Complete Information

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 des...

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Bibliographic Details
Published in:Econometrica 2003-05, Vol.71 (3), p.857-871
Main Authors: Chung, Kim-Sau, Ely, Jeffrey C.
Format: Article
Language:English
Subjects:
Applications
Applied sciences
Decision theory. Utility theory
Determinism
Econometrics
Economic models
Economic theory
Economic uncertainty
Equilibrium
Exact sciences and technology
Game theory
Implementation
Information
Insurance, economics, finance
Integers
Lotteries
Mathematical methods
Mathematical monotonicity
Mathematics
Nash equilibrium
near-complete information
Necessary conditions
Operational research and scientific management
Operational research. Management science
Pay-off
Preferences
Probability and statistics
Sciences and techniques of general use
Social choice
Statistics
Studies
Sufficiency and information
undominated Nash equilibrium
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Summary: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.
ISSN:0012-9682
1468-0262
DOI:10.1111/1468-0262.00428