When is multidimensional screening a convex program?

• 成果类型: Article
• 署名作者: Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.
• 署名单位: University of Toronto; University of Texas System; University of Texas Austin; University of British Columbia
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2010.11.006
• 发表日期: 2011
• 页码: 454-478
• 关键词: principal agent; asymmetric information; monopoly; nonlinear pricing; price discrimination; Multidimensional signalling; screening; Social welfare maximization under budget constraint; optimal taxation; incentive compatibility; mechanism design; exclusion; Bunching; Robustness; Private imperfect incomplete information; Optimal transportation; Ma-Trudinger-Wang; Cross-curvature

摘要

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirdees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x, y) of product type y to agent type x - and on the principal's costs c(y) - which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal's problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal's optimal strategy - and similarly of the strategy maximizing the expected welfare of the agents when the principal's profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang's necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models. (C) 2011 Elsevier Inc. All rights reserved.