Gross substitutes and endowed assignment valuations
نویسندگان
چکیده
We show that the class of preferences satisfying the Gross Substitutes condition of Kelso and Crawford (1982) is strictly larger than the class of Endowed Assignment Valuations of Hatfield and Milgrom (2005), thus resolving the open question posed by the latter paper. In particular, our result implies that not every valuation function that satisfies the Gross Substitutes condition can be “decomposed” into a combination of unit-demand valuations.
منابع مشابه
When Are Welfare Guarantees Robust?
Computational and economic results suggest that social welfare maximization and combinatorial auction design are much easier when bidders’ valuations satisfy the “gross substitutes” condition. The goal of this paper is to evaluate rigorously the folklore belief that the main take-aways from these results remain valid in settings where the gross substitutes condition holds only approximately. We...
متن کاملCS 364 B : Frontiers in Mechanism Design Lecture # 5 : The Gross Substitutes Condition ∗
Thus far, we’ve studied four scenarios that admit tractable auctions that maximize welfare subject to strong incentive guarantees. The first two were simple enough that English auctions did the trick. The last two scenarios — unit-demand valuations with non-identical items, and downward-sloping valuations with identical items — were not so simple. While we got everything we wanted, we had to wo...
متن کاملCS364B: Frontiers in Mechanism Design Lecture #11: Undominated Implementations and the Shrinking Auction∗
Part I of the course focused on special cases where we can achieve all three properties — gross substitutes (GS) valuations and special cases thereof. In Part II of the course, we focused on more general valuation classes in which the exact version of the second property is already incompatible with the third (assuming P 6= NP ). We focused further on special cases where, ignoring incentive con...
متن کاملOn Welfare Approximation and Stable Pricing
We study the power of item-pricing as a tool for approximately optimizing social welfare in a combinatorial market. We consider markets with m indivisible items and n buyers. The goal is to set prices to the items so that, when agents purchase their most demanded sets simultaneously, no conflicts arise and the obtained allocation has nearly optimal welfare. For gross substitutes valuations, it ...
متن کاملConditional Equilibrium Outcomes via Ascending Price Processes∗
A Walrasian equilibrium in an economy with non-identical indivisible items exists only for small classes of players’ valuations (mostly “gross substitutes” valuations), and may not generally exist even with decreasing marginal values. This paper studies a relaxed notion, “conditional equilibrium”, that requires individual rationality and “outward stability”, i.e., a player will not want to add ...
متن کامل