Thesis on implementation under ambiguity

Liu, Zhiwei

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https://hdl.handle.net/2142/49747 Copy

Description

Title

Thesis on implementation under ambiguity

Author(s)

Liu, Zhiwei

Issue Date

2014-05-30T17:07:40Z

Director of Research (if dissertation) or Advisor (if thesis)

Yannelis, Nicholas C.

Doctoral Committee Chair(s)

Yannelis, Nicholas C.

Committee Member(s)

• Villamil, Anne P.
• Krasa, Stefan
• Polborn, Mattias K.

Department of Study

Economics

Discipline

Economics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Maximin Preferences
• Implementation
• Maximin Equilibrium
• Individually Rational and Maximin Efficient Notions
• Maximin Rational Expectations Equilibrium

Abstract

The thesis consists of three chapters. In Chapter one (with professor Nicholas Yannelis), we introduce the idea of implementation under ambiguity. In particular, we study maximin efficient notions of an ambiguous asymmetric information economy (i.e., economies where agents' preferences are maximin). The interest on the maximin efficient notions lies in the fact that they are always incentive compatible (de Castro-Yannelis 2009), a result which is false with Bayesian preferences. A noncooperative notion called maximin equilibrium is introduced which provides a noncooperative foundation for individually rational and maximin efficient notions, for example, maximin core and maximin value allocation. Specifically, we show that given any arbitrary individually rational and ex-ante maximin efficient allocation, there is a direct revelation mechanism that yields the efficient allocation as its unique maximin equilibrium outcome. Thus, an incentive compatible, individually rational and efficient outcome can be reached by means of noncooperative behavior under ambiguity. In Chapter two, we provide a counterexample to the ex-ante efficiency of the maximin rational expectations equilibrium. In particular, we show that a maximin rational expectations equilibrium allocation may not be ex-ante maximin efficient, and therefore it may not be in the maximin core. Another consequence is that the implementation result of Chapter one cannot be applied to the maximin rational expectations equilibrium. Finally, in Chapter three, we show that each maximin rational expectations equilibrium allocation is maximin Nash incentive compatible. Also, we characterize the conditions, under which each maximin rational expectations equilibrium is implementable as a maximin equilibrium. These findings contribute to the desirability of the maximin rational expectations equilibrium notion.

Graduation Semester

2014-05

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http://hdl.handle.net/2142/49747

Copyright and License Information

Copyright 2014 Zhiwei Liu

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