什么时候多维筛选是凸规划？
When is multidimensional screening a convex program?
摘要：
委托人希望与多维分布的代理人进行交易，这些代理人的偏好仅在总体上是已知的。假设一个扭曲（=广义Spence-Mirrlees单交叉）假设和代理只能选择纯策略，我们确定了一个结构性条件的偏好b（x，y）的代理类型x的产品类型y -和委托人的成本c（y）-这是必要的和充分的减少利润最大化问题所面临的委托人凸规划。这是一个关键的一步，使校长的问题在理论上和计算上易于处理，特别是，它使我们能够获得唯一性和稳定性的校长的最佳策略-同样的策略最大化的预期福利的代理人时，校长的盈利能力受到限制。我们称这个条件为非负交叉曲率：它也是（i）保证b-凸函数的集合的凸性的必要和充分条件，（ii）在通过同构的代理和/或产品类型的重新参数化下不变，以及（iii）Ma的加强，Trudinger和Wang的充要条件（A3 w）为了在外部规定的代理和产品的分配之间的对应关系的连续性。我们得到的持久性的经济影响，如垄断的愿望，建立价格如此之高，他们有效地排除了积极的一部分，其潜在的客户，在几乎所有的非负交叉曲线模型。
英文摘要：
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-Mirrlees single-crossing) hypothesis and that agents can choose only pure strategies, we identify a structural condition on the preference b(x,y) of agent type x for product type y -- 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 optimum 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
