Strategic Distinguishability With an Application to Robust Virtual Implementation

50 Pages Posted: 4 Jun 2007

See all articles by Dirk Bergemann

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics; Yale University - Cowles Foundation

Stephen Morris

Princeton University - Department of Economics

Date Written: June 2007

Abstract

In 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.

Keywords: Mechanism design, Virtual implementation, Robust implementation, Rationalizability, Ex-Post incentive compatibility

JEL Classification: C79, D82

Suggested Citation

Bergemann, Dirk and Morris, Stephen Edward, Strategic Distinguishability With an Application to Robust Virtual Implementation (June 2007). Cowles Foundation Discussion Paper No. 1609. Available at SSRN: https://ssrn.com/abstract=991105

Dirk Bergemann (Contact Author)

Yale University - Cowles Foundation - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3592 (Phone)
203-432-2128 (Fax)

HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Stephen Edward Morris

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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