COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1609R

Strategic Distinguishability and Robust Virtual Implementation

Dirk Bergemann and Stephen Morris

March 2006
Revised April 2008

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

[Old title: "Strategic Distinguishability with an Application to Robust Virtual Implementation"]