Interdependent Preferences and Strategic Distinguishability

A universal type space of interdependent expected utility preference types is constructed from higher-order preference hierarchies describing (i) an agent's (unconditional) preferences over a lottery space; (ii) the agent's preference over Anscombe-Aumann acts conditional on the unconditional preferences; and so on. Two types are said to be strategically indistinguishable if they have an equilibrium action in common in any mechanism that they play. We show that two types are strategically indistinguishable if and only if they have the same preference hierarchy. We examine how this result extends to alternative solution concepts and strategic relations between types.Interdependent preferences, Higher-order preference hierarchy, Universal type space, Strategic distinguishability

Interdependent Preferences and Strategic Distinguishability

A universal type space of interdependent expected utility preference types is constructed from higher-order preference hierarchies describing (i) an agent's (unconditional) preferences over a lottery space; (ii) the agent's preference over Anscombe-Aumann acts conditional on the unconditional preferences; and so on. Two types are said to be strategically indistinguishable if they have an equilibrium action in common in any mechanism that they play. We show that two types are strategically indistinguishable if and only if they have the same preference hierarchy. We examine how this result extends to alternative solution concepts and strategic relations between types.Interdependent preferences, Higher-order preference hierarchy, Universal type space, Strategic distinguishability

Strategic Distinguishability and Robust Virtual Implementation

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.Mechanism design, Virtual implementation, Robust implementation, Rationalizability, Ex-post incentive compatibility

Robust Virtual Implementation

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 payoff 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 payoff types receive the same allocation. We show that ex post incentive compatibility and robust measurability are necessary and sufficient for robust virtual implementation.Mechanism design, Virtual implementation, Robust implementation, Rationaliz­ability, Ex-post incentive compatibility

Robust Virtual Implementation

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 payoff 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 payoff types receive the same allocation. We show that ex post incentive compatibility and robust measurability are necessary and sufficient for robust virtual implementation

Robust Mechanism Design: An Introduction

This essay is the introduction for a collection of papers by the two of us on "Robust Mechanism Design" to be published by World Scientific Publishing. The appendix of this essay lists the chapters of the book. The objective of this introductory essay is to provide the reader with an overview of the research agenda pursued in the collected papers. The introduction selectively presents the main results of the papers, and attempts to illustrate many of them in terms of a common and canonical example, the single unit auction with interdependent values. In addition, we include an extended discussion about the role of alternative assumptions about type spaces in our work and the literature, in order to explain the common logic of the informational robustness approach that unifies the work in this volume.Mechanism design, Robust mechanism design, Common knowledge, Universal type space, Interim equilibrium, Ex post equilibrium, Dominant strategies, Rationalizability, Partial implementation, Full implementation, Robust implementation