Strategic Distinguishability and Robust Virtual Implementation
AbstractIn a general interdependent preference environment, we characterize when two payoff types can be distinguished by their rationalizable strategic choices without any prior knowledge of their beliefs and higher order beliefs. We show that two types are strategically distinguishable if and only if they satisfy a separability condition. The separability condition for each agent essentially requires that there is not too much interdependence in preferences across agents. A social choice function -- mapping payoff type profiles to outcomes -- can be robustly virtually implemented if there exists a mechanism such that every equilibrium on every type space achieves an outcome arbitrarily close to the social choice function: this definition is equivalent to requiring virtual implementation in iterated deletion of strategies that are strictly dominated for all beliefs. The social choice function is robustly measurable if strategically indistinguishable types receive the same allocation. We show that ex post incentive compatibility and robust measurability are necessary and sufficient for robust virtual implementation.
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1609R.
Length: 49 pages
Date of creation: Jun 2007
Date of revision: Apr 2008
Publication status: Published in Theoretical Economics (2009), 4: 45-88
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Find related papers by JEL classification:
- C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-05-05 (All new papers)
- NEP-CDM-2008-05-05 (Collective Decision-Making)
- NEP-CTA-2008-05-05 (Contract Theory & Applications)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dirk Bergemann & Stephen Morris, 2005.
"Robust Implementation: The Role of Large Type Spaces,"
Cowles Foundation Discussion Papers
1519, Cowles Foundation for Research in Economics, Yale University.
- Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
- Dirk Bergemann & Stephen Morris, 2009.
"Robust Implementation in Direct Mechanisms,"
Review of Economic Studies,
Oxford University Press, vol. 76(4), pages 1175-1204.
- Bergemann, Dirk & Stephen Morris, 2006. "Robust Implementation in Direct Mechanisms," Cowles Foundation Discussion Papers 1561RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
- Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Levine's Working Paper Archive 814577000000000109, David K. Levine.
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