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Strategic Distinguishability with an application to Robust Virtual Implementation



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STRATEGIC DISTINGUISHABILITY WITH AN APPLICATION TO ROBUST VIRTUAL IMPLEMENTATION By Dirk Bergemann and Stephen Morris June 2007 COWLES FOUNDATION DISCUSSION PAPER NO 1609 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven Connecticut 06520 8281 http cowles econ yale edu Strategic Distinguishability with an application to Robust Virtual Implementation Dirk Bergemanny Stephen Morrisz First Version March 2006 This Version May 2007 Abstract In a general interdependent preference environment we characterize when two payo 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 payo type pro les 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 de nition 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 su cient for robust virtual implementation Keywords Mechanism Design Virtual Implementation Robust Implementation Rationalizability ExPost Incentive Compatibility Jel Classification C79 D82 This research is partially supported by NSF Grants CNS 0428422 and SES 0518929 We are grateful for discussions with Dilip Abreu Faruk Gul Matt Jackson Eric Maskin Wolfgang Pesendorfer Phil Reny Roberto Serrano and seminar audiences at Chicago Georgetown Penn Princeton Rutgers



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