Weak versus strong domination in a market with indivisible goods

Roth, Alvin E.; Postlewaite, Andrew

doi:10.1016/0304-4068(77)90004-0

Cited by 315 publications

(198 citation statements)

References 3 publications

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“…In Section 3 we use these conditions as the basis for an O( √ nm) algorithm for finding a maximum Pareto optimal matching. This algorithm extends the Top Trading Cycles Method due to Gale [14], which has been the focus of much attention, particularly in the game theory and economics literature [14,12,11,15,2]. We then show that any improvement to the complexity of our algorithm would imply an improved algorithm for finding a maximum matching in a bipartite graph.…”

Section: Introductionmentioning

confidence: 81%

“…We assume that each agent a ∈ A ranks in order of preference a subset of H (the acceptable goods for a) and that monetary compensations are not possible. In the literature the situation in which each agent initially owns one good is known as a housing market [14,12,11]. When there are no initial property rights, we obtain the house allocation problem [8,16,1].…”

Section: Introductionmentioning

confidence: 99%

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Pareto Optimality in House Allocation Problems

Abraham

Cechlárová

Manlove

et al. 2004

Lecture Notes in Computer Science

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Abstract. We study Pareto optimal matchings in the context of house allocation problems. We present an O( √ nm) algorithm, based on Gale's Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is NP-hard, though approximable within a factor of 2. We then show that there exist Pareto optimal matchings of all sizes between a minimum and maximum cardinality Pareto optimal matching. Finally, we introduce the concept of a signature, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching.

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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Pareto Optimality in House Allocation Problems

Abraham

Cechlárová

Manlove

et al. 2004

Lecture Notes in Computer Science

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“…. Roth and Postlewaite (1977) define an allocation a to be stable if a ∈ C(a) holds. Likewise, we define an allocation a to be strictly stable if a ∈ SC(a).…”

Section: The Market With Indivisible Goodsmentioning

confidence: 99%

“…(Shapley and Scarf, 1974;Wako, 1984;Roth and Postlewaite, 1977) Fact 2 CA(a) is not empty; thus C(a) is also non-empty. (Shapley and Scarf, 1974) Fact 3 SC(a) may be empty.…”

Section: The Market With Indivisible Goodsmentioning

confidence: 99%

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Dynamics, Stability, and Foresight in the Shapley-Scarf Housing Market

Kamijo

Kawasaki

2009

SSRN Journal

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SummaryWhile most of the literature starting with Shapley and Scarf (1974) have considered a static exchange economy with indivisibilities, this paper studies the dynamics of such an economy. We find that both the dynamics generated by competitive equilibrium and the one generated by weakly dominance relation, converge to a set of allocations we define as strictly stable, which we can show to exist. Moreover, we show that even when only pairwise exchanges between two traders are allowed, the strictly stable allocations are attained eventually if traders are sufficiently farsighted. Shapley and Scarf (1974) have considered a static exchange economy with indivisibilities, this paper studies the dynamics of such an economy. We find that both the dynamics generated by competitive equilibrium and the one generated by weakly dominance relation, converge to a set of allocations we define as strictly stable, which we can show to exist. Moreover, we show that even when only pairwise exchanges between two traders are allowed, the strictly stable allocations are attained eventually if traders are sufficiently farsighted. KeywordsJEL classification: D78, C71

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Wireless Networks and Matching Theory

2016

Advanced Wireless Networks

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Weak versus strong domination in a market with indivisible goods

Cited by 315 publications

References 3 publications

Pareto Optimality in House Allocation Problems

Pareto Optimality in House Allocation Problems

Dynamics, Stability, and Foresight in the Shapley-Scarf Housing Market

Wireless Networks and Matching Theory

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