Unified gross substitutes and inverse isotonicity for equilibrium problems
提出了对应关系的替代性概念，证明满足统一总替代和非逆转性的供给对应，其均衡价格集是子格且随数量递增，并应用于逆需求、利润最大化、竞争均衡、匹配博弈等问题。
We introduce a notion of substitutability for correspondences and establish a monotone comparative static result. More precisely, we introduce the notions of unified gross substitutes and nonreversingness and show that if Q: P ⇉ Q is a supply correspondence defined on a set of prices P , which is a sublattice of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mrow> <a:mi mathvariant="double-struck">R</a:mi> </a:mrow> <a:mrow> <a:mi>N</a:mi> </a:mrow> </a:msup> </a:math>, and Q satisfies these two properties, then the set of equilibrium prices Q −1 ( q ) associated with a vector of quantities q ∈ Q is a sublattice of P and is increasing (in the strong set order) in q . We establish connections between our notion of substitutes and existing notions, and examine applications such as the structure of inverse demand, profit maximization, the structure of competitive equilibria, matching games, hedonic pricing, and routing problems.