逆向选择的对偶与自由边界方法
A duality and free boundary approach to adverse selection
AI总结：
本文针对多维逆向选择问题，通过识别对偶最小化问题刻画了Rochet-Choné凹最大化问题的解，并利用对偶性将其平方实例转化为新颖的自由边界问题，首次给出了被忽视市场段的分析描述。
摘要：
逆向选择是委托代理问题的一个版本，包含垄断者非线性定价，其中已知成本的垄断者面对偏好仅在总体上已知的潜在消费者群体，寻求利润最大化的价格菜单。对于多维代理和产品空间，Rochet和Choné（1998）假设代理偏好结合了产品和代理参数的双线性性以及对价格的拟线性敏感性，将此问题重新表述为凸函数集合上的凹最大化。我们通过识别对偶最小化问题来刻画该问题的解。这种对偶性使我们能将Rochet-Choné平方实例的求解转化为一个新颖的自由边界问题，首次给出了一个被忽视市场段的分析描述。
英文摘要：
Adverse selection is a version of the principal-agent problem that includes monopolist nonlinear pricing, where a monopolist with known costs seeks a profit-maximizing price menu facing a population of potential consumers whose preferences are known only in the aggregate. For multidimensional spaces of agents and products, Rochet and Choné (1998) reformulated this problem to a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a quasilinear sensitivity to prices. We characterize solutions to this problem by identifying a dual minimization problem. This duality allows us to reduce the solution of the square example of Rochet-Choné to a novel free boundary problem, giving the first analytical description of an overlooked market segment.
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