多维特征市场均衡解的存在唯一性与有效性
Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimenstional types
摘要：
我们研究享乐市场的均衡，当消费者和供应商有保留效用时，效用函数相对于价格是可分离的。有一种不可分割的商品，它有不同的质量;每个消费者购买0或1个单位，每个供应商出售0或1个单位。消费者类型、供应商类型和质量可以是离散的，也可以是连续的，在这种情况下，它们可以是多维的。价格起着双重作用：它们将一些代理人挡在市场之外，并将剩余的代理人配对。我们定义了均衡价格和均衡分布，我们证明了均衡存在，我们研究了均衡价格和分布在多大程度上是唯一的，我们证明了均衡是有效的。在特定的情况下，当有一个连续的类型，并满足广义Spence-Mirrlees条件，我们证明了存在一个纯平衡，需求分布实际上是需求函数，我们在多大程度上它是唯一的。证明依赖于凸分析，并照顾已给出的例子来说明理论。
英文摘要：
We study equilibrium in hedonic markets, when consumers and suppliers have reservation utilities, and the utility functions are separable with respect to price. There is one indivisible good, which comes in different qualities; each consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types, supplier types and qualities can be either discrete of continuous, in which case they are allowed to be multidimensional. Prices play a double role: they keep some agents out of the market, and they match the remaining ones pairwise. We define equilibrium prices and equilibrium distributions, and we prove that equilibria exist, we investigate to what extend equilibrium prices and distributions are unique, and we prove that equilibria are efficient. In the particular case when there is a continuum of types, and a generalized Spence-Mirrlees condition is satisfied, we prove the existence of a pure equilibrium, where demand distributions are in fact demand functions, and we show to what extent it is unique. The proofs rely on convex analysis, and care has been given to illustrate the theory with examples.
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