Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities
通过几何结构与效用函数之间的等价定理，将估值分类为“需求类型”，并推广了竞争均衡存在性的结果，发现纯互补偏好比纯替代偏好更能保证均衡存在，还提出了交点计数定理来检验均衡存在性，应用包括匹配和英格兰银行的产品组合拍卖。
An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into “Demand Types” incorporates existing definitions (substitutes, complements, “strong substitutes,” etc.) and permits new ones. Our Unimodularity Theorem generalizes previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a “demand type.” Contrary to popular belief, equilibrium is guaranteed for more classes of purely‐complements than of purely‐substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition‐formation, and the “Product‐Mix Auction” introduced by the Bank of England in response to the financial crisis.