Optimal Combinatorial Mechanism Design
نویسنده
چکیده
We study an adverse selection model in which a principal will allocate a set of nonidentical objects among privately informed agents. Combinatorial auctions provide an important class of examples. Agents have private information that is parametrized by a one dimensional type. The principal collects type reports from the agents, computes their valuations for di¤erent sets, and then decides on an allocation and payments so as to maximize revenue. Working with one dimensional private information allows us to isolate the model from the well known problems of multidimensional types and focus on the problems associated with multidimensional outcomes. In particular we reformulate the optimal mechanism design problem using the methodology of Myerson (1981) and identify regularity conditions under which the reformulated problem can be solved without the constraints. We nd that the solution to a regular problem involves solving a combinatorial optimization problem. We provide conditions under which the mechanism design problem is regular and obtain results for two large classes of valuation functions. The rst class consists of functions which satisfy an increasing di¤erences property. All supermodular valuations belong to this class. The second class consists of functions which scalarize sets independently from types and have a single crossing property. This class involves many interesting examples, as well as some valuations that are not in the rst class. Keywords: Mechanism design, Adverse selection, Combinatorial auctions, Supermodularity, Single crossing JEL Classi cation: C72, D44, D82. 1Many thanks are due to my advisor Richard McLean for his invaluable guidance. I also bene tted from several helpful discussions with Colin Campbell and Tomas Sjöström. All remaining errors are, of course, mine. 2Email: [email protected].
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تاریخ انتشار 2006