Δ-Substitute Preferences and Equilibria with Indivisibilities

Thành Nguyen, Rakesh Vohra

Abstract: Gross substitutes for quasi-linear preferences is characterized by the single improvement property, which says an agent can improve upon a sub-optimal bundle by adding or dropping a single item, or exchanging one item for another. We extend this notion in two ways: by allowing for non-quasi-linear preferences and the exchange of up to Delta items. Our results connect the improvement property with the geometry of the choice correspondence. We derive prices at which the excess demand for each good is at most Delta-1 and provide applications to the design of pseudo-markets for allocating indivisible resources.