Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
Multi-unit Auctions with Budget Limits
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
General auction mechanism for search advertising
Proceedings of the 18th international conference on World wide web
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
An expressive mechanism for auctions on the web
Proceedings of the 20th international conference on World wide web
Computation and incentives of competitive equilibria in a matching market
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Sponsored search, market equilibria, and the Hungarian Method
Information Processing Letters
Bidder optimal assignments for general utilities
Theoretical Computer Science
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Consider a market with n unit demand buyers and m sellers, each selling one unit of an indivisible good. The buyers specify their preferences over items via utility functions uij(pj), which is the utility of buyer i for item j when its price is pj. So far, this is the classic Shapley-Shubik assignment model [Shapley and Shubik 1971] which captures a variety of matching markets including housing markets and ad auctions [Edelman et al. 2007], except for the extension to general utility functions instead of the quasi-linear utilities in the original model. Shapley and Shubik show that a competitive equilibrium always exists in their model, and later work [Crawford and Knoer 1981, Quinnzi 1984, Gale 1984] shows that a competitive equilibrium must also exist for the model with general utility functions uij(·), provided these uij(·) are strictly decreasing and continuous everywhere.