Belief Free Incomplete Information Games

Author : Takuro Yamashita
Publisher : Stanford University
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.F/5 ( download)

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Download or read book A Necessary Condition for Robust Implementation written by Takuro Yamashita and published by Stanford University. This book was released on 2011 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanism design theory examines which social objectives (such as efficiency, fairness, stability, and so on) can be achieved when agents have private information. In most of the papers in the mechanism design literature, it has been the standard approach to assume that the agents play a Bayesian-Nash equilibrium (typically with a ``common prior'') to predict the possible outcomes of mechanisms. However, this approach is often criticized due to its sensitivity of prediction to the assumptions on the agents' beliefs. Given these criticisms, some researchers have investigated robust mechanisms to uncertainty about the agents' beliefs, but the standard approach is to restrict attention to dominant-strategy mechanisms. This approach proves to be restrictive, especially in settings that require a balanced budget. In this dissertation, we consider similar robust approaches, but we do not restrict attention only to dominant-strategy mechanisms. In Chapter 2, we provide an example that illustrates a difference between the dominant strategy approach and the other robust implementation approaches. Specifically, we consider expected welfare maximization in a bilateral trading example with voluntary participation and balanced budget. Chapter 3 provides some general findings. First, we show that any social choice correspondence that is implementable in admissibility must have a ``tree dominance property'': For any profile of ``directed trees'' on each agent's type space, the social choice correspondence must have a selection that satisfies dominant-strategy incentive compatibility along all edges of these trees. Also, we discuss the relationships among different robust implementation concepts. In Chapter 4, we apply these theoretical findings to some economic examples. In general, the tree dominance property may not be a sufficient condition. In applications, we guess which tree dominance conditions are the ``binding'' conditions, and solve a relaxed problems subject to those tree dominance conditions. In some cases, the allocation rule that solves the relaxed problem is proved to be dominant-strategy incentive compatible, which means that dominant-strategy mechanisms cannot be robustly improvable. Even if the solution is not dominant-strategy incentive compatible, we can sometimes verify that this allocation rule can be used as a revelation mechanism that actually robustly implements the desired social choice correspondence. As specific applications, we study (i) bilateral trading settings with balanced budget, (ii) quasi-linear environments without balanced budget, and (iii) implementation of unique desirable allocation rules.