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Probabilistic stable rules and Nash equilibrium in two-sided matching problems

Yazici, A.

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Abstract

We study many-to-many matching with substitutable and cardinally monotonic preferences. We analyze stochastic dominance (sd) Nash equilibria of the game induced by any probabilistic stable matching rule. We show that a unique match is obtained as the outcome of each sd-Nash equilibrium. Furthermore, individual-rationality with respect to the true preferences is a necessary and sufficient condition for an equilibrium outcome. In the many-to-one framework, the outcome of each equilibrium in which firms behave truthfully is stable for the true preferences. In the many-to-many framework, we identify an equilibrium in which firms behave truthfully and yet the equilibrium outcome is not stable for the true preferences. However, each stable match for the true preferences can be achieved as the outcome of such equilibrium.

Citation

Yazici, A. (2017). Probabilistic stable rules and Nash equilibrium in two-sided matching problems. International Journal of Game Theory, 46(1), 103-124. https://doi.org/10.1007/s00182-015-0525-3

Journal Article Type Article
Acceptance Date Dec 22, 2015
Online Publication Date Jan 25, 2016
Publication Date Mar 1, 2017
Deposit Date Dec 29, 2015
Publicly Available Date Jan 25, 2017
Journal International Journal of Game Theory
Print ISSN 0020-7276
Electronic ISSN 1432-1270
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 46
Issue 1
Pages 103-124
DOI https://doi.org/10.1007/s00182-015-0525-3
Keywords Probabilistic rules, Stability, Nash equilibrium, Substitutability, Cardinal monotonicity.
Public URL https://durham-repository.worktribe.com/output/1395872

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