【主讲】Jacob Goeree 教授 (University of Zurich)
【主题】A Geometric Approach to Mechanism Design
【时间】2011年12月6日 (周二) 15：30-17：00
【地点】上海财经大学经济学院楼701室
【语言】英文
【摘要】An important result in convex analysis is the duality between a closed convex set and its support function. We exploit this duality to develop a geometric approach to mechanism design. For a general class of social choice problems we characterize the feasible set, which is closed and convex, and its support function. We next provide a geometric interpretation of incentive compatibility and refine the support function to include incentive constraints using arguments from majorization theory. The optimal mechanism can subsequently be derived from the support function using Hotelling's lemma. We demonstrate the usefulness of our geometric approach in several ways. First, for single-unit private-value auctions, the support-function inequalities for the feasible set yield the Maskin-Riley-Matthews-Border conditions characterizing reduced form implementability. Importantly, our approach generates their analogues for general social choice problems. Second, we provide a geometric proof of the equivalence of Bayesian and dominant strategy implementation by showing that the sets that remain after imposing Bayesian or dominant strategy incentive compatibility coincide. Third, we demonstrate how other types of constraints can be easily incorporated, which allows us to replicate and extend a number of important results in the mechanism design literature including optimal multi-unit auctions when bidders have capacity constraints or non-linear valuations, bargaining with ex ante or ex post budget balance, and public goods provision. Finally, we discuss how our geometric approach can be applied when the paper's main assumptions, i.e. linear value functions and independent, private, and one-dimensional types, are relaxed. To illustrate, we show that with interdependent valuations the equivalence between Bayesian and dominant strategy implementation breaks down but our approach still produces the second-best outcomes for both types of incentive constraints.
