Random Paths to Stability in Two-Sided Matching

Roth, Alvin E.; Vate, John H. Vande

doi:10.2307/2938326

Cited by 304 publications

(234 citation statements)

References 6 publications

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“…While there are cycles in the marriage problem there are no closed cycles. That follows from the main result in Roth and Vande Vate [35], which in the network language says that from each network there is a simultaneous improving path leading to some core stable network. This implies (from Lemma 2 here) that all stochastically stable networks will be core stable networks.…”

Section: Simultaneous Improving Pathsmentioning

confidence: 72%

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The Evolution of Social and Economic Networks

Jackson¹,

Watts²

2002

Journal of Economic Theory

833

755

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We examine the dynamic formation and stochastic evolution of networks connecting individuals. The payoff to an individual from an economic or social activity depends on the network of connections among individuals. Over time individuals form and sever links connecting themselves to other individuals based on the improvement that the resulting network offers them relative to the current network. In addition to intended changes in the network there is a small probability of unintended changes or errors. Predictions can be made regarding the likelihood that the stochastic process will lead to any given network at some time, where the stochastic process selects from among the statically stable networks and cycles. We apply these results to examples including the Gale-Shapley marriage problem. Thus the paper achieves two goals. First, it outlines a dynamic solution concept for networks. Second, it applies this concept to matching problems. Journal of Economic Literature Classification Numbers: A14, D20, J00. © 2002 Elsevier Science (USA)

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Section: Simultaneous Improving Pathsmentioning

confidence: 72%

“…The existence of a marriage cycle was first demonstrated by Knuth [28] and is also discussed in Roth and Vande Vate [35]. While there are cycles in the marriage problem there are no closed cycles.…”

Section: Simultaneous Improving Pathsmentioning

confidence: 96%

The Evolution of Social and Economic Networks

Jackson¹,

Watts²

2002

Journal of Economic Theory

833

755

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“…Our models are similar to Roth and Vande Vate (1990) in this respect. Roth and Vande Vate (1990) consider a transition of matching pairs in marriage market where in each step, one of the blocking coalitions is randomly chosen and selected coalition changes the current matching to the others by the blocking deviation. They show that this dynamics converges with probability one to a stable matching.…”

Section: Introductionmentioning

confidence: 48%

“…The following example shows the negative answer to this question. This is quite in contrast with Roth and Vande Vate (1990) and Diamantoudi et al (2004) that respectively consider the dynamics in the marriage problem and the roommate problem and show that the convergent results to the stable outcomes holds in these environments even though they do not consider deviation of more than two players coalition. Trader 2 : w 3 2 w 2 2 w 1 Trader 3 : w 1 3 w 3 3 w 2…”

Section: Pairwise Exchange and Foresightmentioning

confidence: 57%

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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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The Effects of the Change in the NRMP Matching Algorithm

Roth¹,

Peranson²

1997

JAMA

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The existing NRMP algorithm and the newly designed applicant-proposing algorithm perform similarly. Both algorithms make it sensible for applicants and residency programs to arrange their ROLs based solely on their preferences for possible matches. The choice of algorithms will systematically affect the matches of only a small group of applicants (<0.1%). The NRMP's recent decision to use the applicant-proposing algorithm starting in 1998 reflects a judgment about the impact of this difference on applicants and programs.

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Random Paths to Stability in Two-Sided Matching

Cited by 304 publications

References 6 publications

The Evolution of Social and Economic Networks

The Evolution of Social and Economic Networks

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

The Effects of the Change in the NRMP Matching Algorithm

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