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Implementation with Incomplete Information in Exchange Economies

Palfrey, Thomas R. and Srivastava, Sanjay (1989) Implementation with Incomplete Information in Exchange Economies. Econometrica, 57 (1). pp. 115-134. ISSN 0012-9682. http://resolver.caltech.edu/CaltechAUTHORS:20160307-145257973

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Abstract

In this paper, we analyze the problem of designing incentive compatible mechanisms in pure exchange economic environments when agents have incomplete information. The equilibrium concept employed is Bayesian Nash equilibrium and the notion of implemantation is full implementation, which is stronger than the more commonly employed notion of truthful implementation. An allocation rule is truthfully implementable if there exists a direct mechanism to which truth telling is an equilibrium and which yields the allocation rule as its truthful equilibrium outcome. An allocation rule is fully implementable if there exists mechanism which yields the allocation rule as its unique equilibrium outcome. More generally, a set of allocation rules, or a social choice set, is fully implementable if there exist a mechanism whose equilibrium outcomes coincide with the set. This stronger notion of implemention avoids the well known problems of multiple equilibria which arise in direct revelation games. We develop a condition, termed Bayesian monotonicity, which we show is necessary for full implementation. An incentive compatibility condition is also necessary. We prove that Bayesian monotonicity and a slightly stronger incentive compatibility condition are sufficient for full implementation when there are at least three agents. We present several examples of allocation rules which do and do not satisfy our condition. One example is that of an allocation rule which is fully inplementable by an indirect mechanism, but for which every equivalent direct mechanism has multiple equilibrium outcomes.


Item Type:Article
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http://www.jstor.org/stable/1912575JSTORJSOR article
Additional Information:© 1989 The Econometric Society. Manuscript received March, 1985; final revision received February, 1988. We thank Andrew Postlewaite, participants of the BER/CEME/NSF Conference on General Equilibrium Theory, Cambridge, May 1985, and the Northwestern University 1985 Summer Workshop on Strategic Behavior and Competition, for their feedback on earlier versions of this work. We also thank David Kreps and an anonymous referee for helpful suggestions which have greatly improved the paper.
Subject Keywords:Implementation, incomplete information, noncooperative games, incentive compatibility, general equilibrium.
Record Number:CaltechAUTHORS:20160307-145257973
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160307-145257973
Official Citation:Palfrey, Thomas R., and Sanjay Srivastava. 1989. “Implementation with Incomplete Information in Exchange Economies”. Econometrica 57 (1). [Wiley, Econometric Society]: 115–34. doi:10.2307/1912575.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65146
Collection:CaltechAUTHORS
Deposited By: Susan Vite
Deposited On:01 Apr 2016 00:10
Last Modified:01 Apr 2016 00:10

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