Von Neumann–Morgenstern stable sets in matching problems

Ehlers, Lars

doi:10.1016/j.jet.2006.03.006

Cited by 76 publications

(56 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The lattice property is something the stable sets of the assignment game have in common with the stable sets of the one-to-one matching problems (the marriage problem), as proved recently by Ehlers [2].…”

Section: Discussionmentioning

confidence: 88%

Von Neumann–Morgenstern solutions in the assignment market

Núñez

Rafels

2013

Journal of Economic Theory

View full text Add to dashboard Cite

The existence of von Neumann-Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik [11].For each optimal matching between buyers and sellers, Shubik [12] proposed considering the union of the core of the game and the core of the subgames that are compatible with this matching. We prove in the present paper that this set is the unique stable set for the assignment game that excludes thirdparty payments with respect to a fixed optimal matching. Moreover, the stable sets that we characterize, as well as any other stable set of the assignment game, have a lattice structure with respect to the same partial order usually defined on the core.

show abstract

Section: Discussionmentioning

confidence: 88%

Von Neumann–Morgenstern solutions in the assignment market

Núñez

Rafels

2013

Journal of Economic Theory

View full text Add to dashboard Cite

show abstract

“…It differs from the effectivity function used by Ehlers [6], who assumes that a coalition S is effective in the move from a matching µ to a matching µ whenever µ (S) = µ(S), implicitly assuming that a coalition S can force agents not in S to match with different agents. 13 They assume the following effectivity function: A coalition S is effective in the move from a partition π to a partition π if all agents in S form a block in π and the agents who belonged to blocks T in π such that T ∩ S = ∅ stick together and form the blocks T \ S in π .…”

Section: Definition 42 Blocking By Coalitionsmentioning

confidence: 99%

Farsighted Stability with Heterogeneous Expectations

Bloch

Nouweland

2017

SSRN Journal

View full text Add to dashboard Cite

This paper analyzes farsighted stable sets when agents have heterogeneous expectations over the dominance paths. We consider expectation functions satisfying two properties of path-persistence and consistency. We show that farsighted stable sets with heterogeneous expectations always exist and that any singleton farsighted stable set with common expectations is a farsighted stable set with heterogeneous expectations. We characterize singleton farsighted stable sets with heterogeneous expectations in one-to-one matching models and voting models, and show that the relaxation of the hypothesis of common expectations greatly expands the set of states that can be supported as singleton farsighted stable sets. JEL Classification Numbers: C71, D72, D74

show abstract

“…This is an important result, as it proves that the 28 Our result reveals an isomorphism between the permissible sets of blocking pairs for a matching µ and the set of stable matchings in another marriage market. Similarly, Ehlers (2007) makes use of the result of Blair (1984) in order to show that there is an isomorphism between a Von Neumann-Morgenstern stable set in one marriage market and the set of stable matchings in another market (see Ehlers (2007), Remark 2, p. 544).…”

Section: A Workable Measure To Compare Matchingsmentioning

confidence: 99%

“…Finally, Ehlers (2007) adapted Von Neumann-Morgenstern stable sets to marriage markets. A set of matchings is a von Neumann-Morgenstern stable set if it is internally stable and externally stable (for details see Ehlers (2007)).…”

mentioning

confidence: 99%

See 1 more Smart Citation

A Measure to Compare Matchings in Marriage Markets

Biermann

2011

SSRN Journal

View full text Add to dashboard Cite

In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly disruptive subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: The subset is a justied objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison.

show abstract

Von Neumann–Morgenstern stable sets in matching problems

Cited by 76 publications

References 21 publications

Von Neumann–Morgenstern solutions in the assignment market

Von Neumann–Morgenstern solutions in the assignment market

Farsighted Stability with Heterogeneous Expectations

A Measure to Compare Matchings in Marriage Markets

Contact Info

Product

Resources

About