(Near-)Substitute Preferences and Equilibria with Indivisibilities
针对不可分物品市场缺乏竞争均衡的问题，定义了Δ-替代偏好，使得社会近似均衡存在且超额需求有界，Δ=1时竞争均衡存在且允许收入效应，Δ>1则允许更丰富的替代与互补模式，拓展了市场机制的应用范围。
An obstacle to using market mechanisms to allocate indivisible goods is the lack of competitive equilibria (CEs). Arrow and Hahn introduced social-approximate equilibria: price vectors with “small” excess demands. We define preferences called Δ-substitutes, where social-approximate equilibria exist with good-by-good excess demand bounded by 2(Δ−1), independent of economy size. For Δ=1, CEs exist even with income effects. A Δ greater than 1 allows for richer substitutability and complementarity patterns, broadening the scope for market mechanisms to allocate indivisible goods.