A General Framework for Endowment Effects in Combinatorial Markets

Ezra, Tomer; Feldman, Michal; Friedler, Ophir

doi:10.48550/arxiv.1903.11360

Cited by 3 publications

(10 citation statements)

References 22 publications

(45 reference statements)

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“…In this section we show that for any valuation profile, every welfare-maximizing allocation can be supported in a 2PE with a discrepancy of at most m. The proof of Proposition B.1 is similar to the proof of Proposition 7.1 in [9].…”

Section: B An Upper Bound On the Discrepancy Of The Optimal Allocationmentioning

confidence: 72%

“…Babaioff et al [1] showed that every market with submodular valuations admits an endowment equilibrium with at least a half of the optimal welfare. Ezra et al [9] introduced a general framework that captures a wide range of formulations for the endowment effect, and showed that stronger endowment effects can lead to existence of endowment equilibrium also in XOS markets. We show conditions under which one can transform an endowment equilibrium to a 2PE and vice versa.…”

Section: Additional Related Workmentioning

confidence: 99%

“…Ezra et al [9] define a partial order over gain functions: Fix a valuation function v and two gain functions, g and ĝ. Given an endowed set X, we write that g X ≺ ĝX if for all Z ⊆ X, g X (Z | X \ Z) ≤ ĝX (Z | X \ Z).…”

Section: A Weaker Gain Function For Xos Valuationsmentioning

confidence: 99%

“…The Identity (ID) gain function is defined as g X ID (Z) = v(Z) [1]. The Absolute Loss (AL) gain function is defined as g X AL (Z) = v(X) − v(X \ Z) [9]. Ezra et al [9] show that every market with XOS buyers admits an EE with respect to the AL gain function.…”

Section: A Weaker Gain Function For Xos Valuationsmentioning

confidence: 99%

“…Furthermore, one can show that (S, p) is a conditional equilibrium iff (S, p, 0) is a 2PE (see Proposition 3.3). The 2PE notion is related to other relaxations of WE, such as the endowment equilibrium ( [1], [9]), named after the endowment effect, discovered by Nobel laureate Richard Thaler ( [18], [19], [21]), stating that buyers tend to inflate the value of items they own. Moreover, as we show in Section 3.1, 2PE is also related to Nash equilibria of simultaneous item auctions -a simple auction format that attracted much research in the last decade ( [2], [6], [12], [11], [7], [4]).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Two-Price Equilibrium

Feldman¹,

Shabtai²,

Wolfenfeld³

2021

Preprint

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Walrasian equilibrium is a prominent market equilibrium notion, but rarely exists in markets with indivisible items. We introduce a new market equilibrium notion, called two-price equilibrium (2PE). A 2PE is a relaxation of Walrasian equilibrium, where instead of a single price per item, every item has two prices: one for the item's owner and a (possibly) higher one for all other buyers. Thus, a 2PE is given by a tuple (S, p, p) of an allocation S and two price vectors p, p, where every buyer i is maximally happy with her bundle S i , given prices p for items in S i and prices p for all other items. 2PE generalizes previous market equilibrium notions, such as conditional equilibrium, and is related to relaxed equilibrium notions like endowment equilibrium. We define the discrepancy of a 2PE -a measure of distance from Walrasian equilibrium -as the sum of differences pj − pj over all items (normalized by social welfare). We show that the social welfare degrades gracefully with the discrepancy; namely, the social welfare of a 2PE with discrepancy d is at least a fraction 1 d+1 of the optimal welfare. We use this to establish welfare guarantees for markets with subadditive valuations over identical items. In particular, we show that every such market admits a 2PE with at least 1/7 of the optimal welfare. This is in contrast to Walrasian equilibrium or conditional equilibrium which may not even exist. Our techniques provide new insights regarding valuation functions over identical items, which we also use to characterize instances that admit a WE.

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Section: B An Upper Bound On the Discrepancy Of The Optimal Allocationmentioning

confidence: 72%

Section: Additional Related Workmentioning

confidence: 99%

Section: A Weaker Gain Function For Xos Valuationsmentioning

confidence: 99%

Section: A Weaker Gain Function For Xos Valuationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Two-Price Equilibrium

Feldman¹,

Shabtai²,

Wolfenfeld³

2021

Preprint

Self Cite

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show abstract

Two-Price Equilibrium

Feldman

Shabtai

Wolfenfeld

2022

AAAI

Self Cite

View full text Add to dashboard Cite

Walrasian equilibrium is a prominent market equilibrium notion, but rarely exists in markets with indivisible items. We introduce a new market equilibrium notion, called two-price equilibrium (2PE). A 2PE is a relaxation of Walrasian equilibrium, where instead of a single price per item, every item has two prices: one for the item's owner and a (possibly) higher one for all other buyers. Thus, a 2PE is given by a tuple (S,p_high,p_low) of an allocation S and two price vectors p_high,p_low, where every buyer i is maximally happy with her bundle S_i, given prices p_low for items in S_i and prices p_high for all other items. 2PE generalizes previous market equilibrium notions, such as conditional equilibrium, and is related to relaxed equilibrium notions like endowment equilibrium. We define the discrepancy of a 2PE --- a measure of distance from Walrasian equilibrium --- as the sum of differences p_high_j-p_low_j over all items (normalized by social welfare). We show that the social welfare degrades gracefully with the discrepancy; namely, the social welfare of a 2PE with discrepancy d is at least a fraction 1/d+1 of the optimal welfare. We use this to establish welfare guarantees for markets with subadditive valuations over identical items. In particular, we show that every such market admits a 2PE with at least 1/7 of the optimal welfare. This is in contrast to Walrasian equilibrium or conditional equilibrium which may not even exist. Our techniques provide new insights regarding valuation functions over identical items, which we also use to characterize instances that admit a WE.

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Walrasian Equilibria in Markets with Small Demands

Deligkas¹,

Melissourgos²,

Spirakis³

2020

Preprint

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We study the complexity of finding a Walrasian equilibrium in markets where the agents have k-demand valuations, where k is a constant. This means that the maximum value of every agent comes from a bundle of size at most k. Our results are threefold. For unit-demand agents, where the existence of a Walrasian equilibrium is guaranteed, we show that the problem is in quasi-NC. Put differently, we give the first parallel algorithm that finds a Walrasian equilibrium in polylogarithmic time. This comes in striking contrast to all existing algorithms that are highly sequential. For k = 2, we show that it is NP-hard to decide if a Walrasian equilibrium exists even if the valuations are submodular, while for k = 3 the hardness carries over to budget-additive valuations. In addition, we give a polynomial-time algorithm for markets with 2-demand single-minded valuations, or unit-demand valuations. Our last set of results consists of polynomial-time algorithms for k-demand valuations in unbalanced markets; markets where the number of items is significantly larger than the number of agents, or vice versa.

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A General Framework for Endowment Effects in Combinatorial Markets

Cited by 3 publications

References 22 publications

Two-Price Equilibrium

Two-Price Equilibrium

Two-Price Equilibrium

Walrasian Equilibria in Markets with Small Demands

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