On Random Matching Markets: Properties and Equilibria (original) (raw)
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Stable matching in a common generalization of the marriage and assignment models
Discrete Mathematics, 2000
In the theory of two-sided matching markets there are two well-known mod- els: the marriage model (where no money is involved) and the assignment model (where payments are involved). Roth and Sotomayor (1990) asked for an expla- nation for the similarities in behavior between those two models. We address this question by introducing a common generalization that preserves the two
Paths to stability for matching markets with couples
Games and Economic Behavior, 2007
We study two-sided matching markets with couples and show that for a natural preference domain for couples, the domain of weakly responsive preferences, stable outcomes can always be reached by means of decentralized decision making. Starting from an arbitrary matching, we construct a path of matchings obtained from 'satisfying' blocking coalitions that yields a stable matching. Hence, we establish a generalization of Roth and Vande Vate's (1990) result on path convergence to stability for decentralized singles markets. Furthermore, we show that when stable matchings exist, but preferences are not weakly responsive, for some initial matchings there may not exist any path obtained from 'satisfying' blocking coalitions that yields a stable matching. JEL classification: C62, C78, D70.
ArXiv, 2020
In 1962, Gale and Shapley introduced a matching problem between two sets of agents MMM and WWW (men/women, students/universities, doctors/hospitals), who need to be matched by taking into account that each agent on one side of the market has an textitexogenous\textit{exogenous}textitexogenous preference order over the agents of the other side. They defined a matching as stable if no unmatched pair can Pareto improve by matching together. They proved the existence of a stable matching using a "deferred-acceptance" algorithm. Shapley and Shubik in 1971, extended the model by allowing monetary transfers (buyers/sellers, workers/firms). Our article offers a further extension by assuming that matched couples obtain their payoff textitendogenously\textit{endogenously}textitendogenously as the outcome of a strategic-form game they have to play. A matching, together with a strategy profile, is textitexternallystable\textit{externally stable}textitexternallystable if no unmatched pair can form a couple and play a strategy profile in their game that Pareto improves their previous payo...
Stable matchings and preferences of couples
Journal of Economic Theory, 2005
Couples looking for jobs in the same labor market may cause instabilities. We determine a natural preference domain, the domain of weakly responsive preferences, that guarantees stability. Under a restricted unemployment aversion condition we show that this domain is maximal for the existence of stable matchings. We illustrate how small deviations from (weak) responsiveness, that model the wish of couples to be closer together, cause instability, even when we use a weaker stability notion that excludes myopic blocking. Our remaining results deal with various properties of the set of stable matchings for "responsive couples markets," viz., optimality, filled positions, and manipulation. Journal of Economic Literature Classification Numbers: C78; J41.
Stable Matchings for a Generalised Marriage Problem
SSRN Electronic Journal, 2000
We show that a simple generalisation of the Deferred Acceptance Procedure with men proposing due to yields outcomes for a generalised marriage problem, which are necessarily stable. We also show that any outcome of this procedure is Weakly Pareto Optimal for Men, i.e. there is no other outcome which all men prefer to an outcome of this procedure. In a final concluding section of this paper, we consider the problem of choosing a set of multi-party contracts, where each coalition of agents has a non-empty finite set of feasible contracts to choose from. We call such problems, generalised contract choice problems. The model we propose is a generalisation of the model due to Shapley and Scarf (1974) called the housing market. We are able to show with the help of a three agent example, that there exists a generalised contract choice problem, which does not admit any stable outcome.
Analysis of stochastic matching markets
International Journal of Game Theory, 2013
Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? In this paper we are going to provide answers to these and similar questions, posed by economists and computer scientists. In the first part of the paper we give an alternative proof for the theorems by Diamantoudi et al. and Inarra et al. which implies that the corresponding stochastic processes are absorbing Markov chains. Our proof is not only shorter, but also provides upper bounds for the number of steps needed to stabilise the system. The second part of the paper proposes new techniques to analyse the behaviour of matching markets. We introduce the Stable Marriage and Stable Roommates Automaton and show how the probabilistic model checking tool PRISM may be used to predict the outcomes of stochastic interactions between myopic agents. In particular, we demonstrate how one can calculate the probabilities of reaching different matchings in a decentralised market and determine the expected convergence time of the stochastic process concerned. We illustrate the usage of this technique by studying some well-known marriage and roommates instances and randomly generated instances.