Robust Mechanism Design∗ Dirk Bergemann† Stephen Morris‡ First Version: December 2000 This Version: November 2001 Preliminary and incomplete Abstract The implementation literature is often criticized because the mechanisms do not seem to be robust to assumed features of the underlying environment. This paper explores one way of formalizing robustness: fixing the set of pay- off relevant types of each player, we ask whether it is possible to implement a given object on large type spaces (reflecting a lack of common knowledge the environment). We show how equilibrium implementation conditions on the universal type space translates into strong solution concepts on the original types space of payoff relevant types. Keywords: Mechanism Design, Common Knowledge, Universal Type Space, Interim Equilibrium, Ex-Post Equilibrium. Jel Classification: ∗This research is support by NSF Grant #SES-0095321. We are grateful for comments from seminar participants at the Institute for Advanced Study, the Stony Brook Game Theory Conference: Seminar on Contract Theory, and the University of Pennsylvania who heard very preliminary versions of this work. We thank Matt Jackson, Jon Levin, Zvika Neeman, Andrew Postlewaite and especially Bart Lipman for valuable discussions about the universal type space. †Department of Economics, Yale University, 28, Hillhouse Avenue, New Haven, CT 06511,
[email protected]. ‡Department of Economics, Yale University, 30, Hillhouse Avenue, New Haven, CT 06511,
[email protected]. “Game theory has a great advantage in explicitly analyzing the con- sequences of trading rules that presumably are really common knowl- edge; it is deficient to the extent it assumes other features to be com- mon knowledge, such as one agent’s probability assessment about an- other’s preferences or information.