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

Yazici, A.

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