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Supermodular Bayesian Implementation: Learning and Incentive Design

Mathevet, Laurent (2007) Supermodular Bayesian Implementation: Learning and Incentive Design. Social Science Working Paper, 1265. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20170728-171530308

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Abstract

I develop supermodular implementation in incomplete information. Supermodular implementable social choice functions (scf) are scf that are Bayesian implementable with mechanisms that induce a supermodular game. If a mechanism induces a supermodular game, agents may learn to play some equilibrium in a dynamic setting. The paper has two parts. The first part is concerned with sufficient conditions for (truthful) supermodular implementability in quasilinear environments. There, I describe a constructive way of modifying a mechanism so that it supermodularly implements a scf. I prove that, any Bayesian implementable decision rule that satisfies a joint condition with the valuation functions, requiring their composition to produce bounded substitutes, is (truthfully) supermodular implementable. This joint condition is always satisfied on finite type spaces; it is also satisfied by C decision rules and valuation functions on a compact type space. Then I show that allocation-efficient decision rules are (truthfully) supermodular im- plementable with balanced transfers. Third, I establish that C^2 Bayesian implementable decision rules satisfying some dimensionality condition are (truthfully) supermodular implementable with an induced game whose interval prediction is the smallest possible. The second part provides a Supermodular Revelation Principle.


Item Type:Report or Paper (Working Paper)
Additional Information:I am profoundly grateful to the members of my dissertation committee, Federico Echenique, Matt Jackson and Preston McAfee, for their help and encouragement. Special thanks are due to Morgan Kousser, John Ledyard, Thomas Palfrey, Eran Shmaya and David Young for helpful advice and conversations. I also wish to thank Kim Border, Chris Chambers, Bong Chan Koh, Leeat Yariv and seminar participants at Caltech. The Division of Humanities and Social Sciences at Caltech, Matt Jackson and Andrea Mattozzi are gratefully acknowledged for financial support.
Group:Social Science Working Papers
Funders:
Funding AgencyGrant Number
Matthew O. JacksonUNSPECIFIED
Andrea MattozziUNSPECIFIED
Caltech Division of Humanities and Social SciencesUNSPECIFIED
Subject Keywords:Implementation, mechanisms, learning dynamics, stability, strategic complementarities, supermodular games
Classification Code:JEL: C72, D78, D83
Record Number:CaltechAUTHORS:20170728-171530308
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170728-171530308
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79575
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:01 Aug 2017 23:19
Last Modified:01 Aug 2017 23:19

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