Robust Virtual Implementation

Dirk Bergemann and Stephen Morris

Chapter 8 in Robust Mechanism Design:The Role of Private Information and Higher Order Beliefs, 2012, pp 263-317 from World Scientific Publishing Co. Pte. Ltd.

Abstract: 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 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.

Keywords: Mechanism Design; Game Theory; Auction Theory; Implementation; Private Information; First and Higher-Order Belief; BayesNash Equilibrium; Ex Post Equilibrium; Rationalizability; Vickrey-Clarke-Groves Mechanisms; Private Value; Interdependent Value; Common Value; Belief-Free Mechanisms (search for similar items in EconPapers)
JEL-codes: C70 D0 (search for similar items in EconPapers)
Date: 2012
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Related works:
Journal Article: Robust virtual implementation (2009)
Working Paper: Robust Virtual Implementation (2009)
Working Paper: Robust Virtual Implementation (2009)
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