Strategic Distinguishability with an Application to 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 1609.
Length: 49 pages
Date of creation: Jun 2007
Date of revision:
Publication status: Published in Theoretical Economics (2009), 4: 45-88
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Other versions of this item:
- Stephen Morris & Dirk Bergemann, 2007. "Strategic Distinguishability With an Application to Robust Virtual Implementation," Levine's Bibliography 843644000000000149, UCLA Department of Economics.
- C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
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"Robust Implementation: The Role of Large Type Spaces,"
784828000000000116, UCLA Department of Economics.
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"The Role of the Common Prior in Robust Implementation,"
122247000000001574, UCLA Department of Economics.
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- Dirk Bergemann & Stephen Morris, 2007. "The Role of the Common Prior in Robust Implementation," Cowles Foundation Discussion Papers 1628, Cowles Foundation for Research in Economics, Yale University.
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"Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine,"
2007-6, Brown University, Department of Economics.
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