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1.
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. 相似文献
2.
Stable schedule matching under revealed preference 总被引:2,自引:0,他引:2
Baiou and Balinski (Math. Oper. Res., 27 (2002) 485) studied schedule matching where one determines the partnerships that form and how much time they spend together, under the assumption that each agent has a ranking on all potential partners. Here we study schedule matching under more general preferences that extend the substitutable preferences in Roth (Econometrica 52 (1984) 47) by an extension of the revealed preference approach in Alkan (Econom. Theory 19 (2002) 737). We give a generalization of the Gale-Shapley algorithm and show that some familiar properties of ordinary stable matchings continue to hold. Our main result is that, when preferences satisfy an additional property called size monotonicity, stable matchings are a lattice under the joint preferences of all agents on each side and have other interesting structural properties. 相似文献
3.
《Games and Economic Behavior》2007,58(1):154-171
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 [Roth, A.E., Vande Vate, J.H., 1990. Random paths to stability in two-sided matching. Econometrica 58, 1475–1480] 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. 相似文献
4.
We show that for any roommate market the set of stochastically stable matchings coincides with the set of absorbing matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts have been proposed to extend the core to all roommate markets (including those with an empty core). An important implication of our results is that the set of absorbing matchings is the only solution concept that is core consistent and shares the stochastic stability characteristic with the core. 相似文献
5.
We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.Roth and Sotomayor (1990) showed that equilibrium outcomes can be unstable. We prove that any stable matching is obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the ‘rural hospital theorem’ cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the equilibrium that is reached and (b) welfare levels are not bounded by the optimal stable matchings (with respect to the true preferences). 相似文献
6.
Von Neumann-Morgenstern stable sets in matching problems 总被引:1,自引:0,他引:1
Lars Ehlers 《Journal of Economic Theory》2007,134(1):537-547
The following properties of the core of a one-to-one matching problem are well-known: (i) the core is non-empty; (ii) the core is a distributive lattice; and (iii) the set of unmatched agents is the same for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (Von Neumann-Morgenstern) stable sets in one-to-one matching problems. We show that a set V of matchings is a stable set of a one-to-one matching problem only if V is a maximal set satisfying the following properties: (a) the core is a subset of V; (b) V is a distributive lattice; and (c) the set of unmatched agents is the same for all matchings belonging to V. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b), and (c). 相似文献
7.
Two-sided matching with interdependent values 总被引:1,自引:0,他引:1
Archishman Chakraborty 《Journal of Economic Theory》2010,145(1):85-105
We introduce and study two-sided matching with incomplete information and interdependent valuations on one side of the market. An example of such a setting is a matching market between colleges and students in which colleges receive partially informative signals about students. Stability in such markets depends on the amount of information about matchings available to colleges. When colleges observe the entire matching, a stable matching mechanism does not generally exist. When colleges observe only their own matches, a stable mechanism exists if students have identical preferences over colleges, but may not exist if students have different preferences. 相似文献
8.
《Games and Economic Behavior》2010,69(2):773-780
In this note, we demonstrate that the problem of “many-to-one matching with (strict) preferences over colleagues” is actually more difficult than the classical many-to-one matching problem, “matching without preferences over colleagues.” We give an explicit reduction of any problem of the latter type to a problem of the former type. This construction leads to the first algorithm which finds all stable matchings in the setting of “matching without preferences over colleagues,” for any set of preferences. Our construction directly extends to generalized matching settings. 相似文献
9.
《Games and Economic Behavior》2003,42(1):91-100
In this note we introduce weak stability, a relaxation of the concept of stability for the marriage model by assuming that the agents are no longer myopic in choosing a blocking pair. The new concept is based on threats within blocking pairs: an individually rational matching is weakly stable if for every blocking pair one of the members can find a more attractive partner with whom he forms another blocking pair for the original matching. Our main result is that under the assumption of strict preferences, the set of weakly stable and weakly efficient matchings coincides with the bargaining set of Zhou (1994, Games Econ. Behav. 6, 512–526) for this context. 相似文献
10.
Ahmet Alkan 《Economic Theory》2002,19(4):737-746
Summary. For a two-sided multipartner matching model where agents are given by path-independent choice functions and no quota restrictions,
Blair [7] had shown that stable matchings always exist and form a lattice. However, the lattice operations were not simple
and not distributive. Recently Alkan [3] showed that if one introduces quotas together with a monotonicity condition then
the set of stable matchings is a distributive lattice under a natural definition of supremum and infimum for matchings. In
this study we show that the quota restriction can be removed and replaced by a more general condition named cardinal monotonicity and all the structural properties derived in [3] still hold. In particular, although there are no exogenous quotas in the
model there is endogenously a sort of quota; more precisely, each agent has the same number of partners in every stable matching.
Stable matchings also have the polarity property (supremum with respect to one side is identical to infimum with respect to the other side) and a property we call
{\it complementarity}.
Received: May 5, 2000; revised version: January 25, 2001 相似文献
11.
We analyze absorbing sets as a solution for roommate problems with strict preferences. This solution provides the set of stable matchings when it is non-empty and some matchings with interesting properties otherwise. In particular, all matchings in an absorbing set have the greatest number of agents with no incentive to change partners. These “satisfied” agents are paired in the same stable manner. In the case of multiple absorbing sets we find that any two such sets differ only in how satisfied agents are matched with each other. 相似文献
12.
Hedonic pricing with quasi-linear preferences is shown to be equivalent to stable matching with transferable utilities and
a participation constraint, and to an optimal transportation (Monge–Kantorovich) linear programming problem. Optimal assignments
in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality;
their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with
type. Under a generalized Spence-Mirrlees condition (also known as a twist condition) the assignments are shown to be unique
and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, connected type spaces such
as the circle, there is a topological obstruction to purity, but we give a weaker condition still guaranteeing uniqueness
of the stable match. 相似文献
13.
We characterize the core many-to-one matchings as fixed points of a map. Our characterization gives an algorithm for finding core allocations; the algorithm is efficient and simple to implement. Our characterization does not require substitutable preferences, so it is separate from the structure needed for the non-emptiness of the core. When preferences are substitutable, our characterization gives a simple proof of the lattice structure of core matchings, and it gives a method for computing the join and meet of two core matchings. 相似文献
14.
Alexander Westkamp 《Journal of Economic Theory》2010,145(5):1724-1738
Ostrovsky (2008) [9] develops a theory of stability for a model of matching in exogenously given networks. For this model a generalization of pairwise stability, chain stability, can always be satisfied as long as agents' preferences satisfy same side substitutability and cross side complementarity. Given this preference domain I analyze the interplay between properties of the network structure and (cooperative) solution concepts. The main structural condition is an acyclicity notion that rules out the implementation of trading cycles. It is shown that this condition and the restriction that no pair of agents can sign more than one contract with each other are jointly necessary and sufficient for (i) the equivalence of group and chain stability, (ii) the core stability of chain stable networks, (iii) the efficiency of chain stable networks, (iv) the existence of a group stable network, and (v) the existence of an efficient and individually stable network. These equivalences also provide a rationale for chain stability in the unrestricted model. The (more restrictive) conditions under which chain stability coincides with the core are also characterized. 相似文献
15.
This article presents a brief survey of two‐sided matching. We introduce the reader to the problem of two‐sided matching in the context of the college admission model and explain two central requirements for a matching mechanism: stability and non‐manipulability. We show how the frequently used ‘Boston Mechanism’ fails these key requirements and describe how an alternative, the Deferred Acceptance Algorithm, leads to stable matchings but fails to be non‐manipulable in general. A third mechanism, the Top Trading Cycle, is efficient and non‐manipulable when only one side of the match acts strategically. We also discuss some applications of matching theory. 相似文献
16.
Mustafa O?uz Afacan 《Games and Economic Behavior》2012,74(1):394-398
We introduce the notion of group robust stability which requires robustness against a combined manipulation, first misreporting preferences and then rematching, by any group of students in the school choice type of matching markets. Our first result shows that there is no group robustly stable mechanism even under acyclic priority structures. Next, we define a weak version of group robust stability, called weak group robust stability. Our main theorem, then, proves that there is a weakly group robustly stable mechanism if and only if the priority structure of schools is acyclic, and in that case, it coincides with the student-optimal stable mechanism. 相似文献
17.
In this study we present a simple mechanism in a many-to-one matching market where multiple costless applications are allowed. The mechanism is based on the principles of eligibility and priority and it implements the set of stable matchings in Subgame Perfect Nash Equilibrium. We extend the analysis to a symmetric mechanism where colleges and students interchange their roles. This mechanism also implements the set of stable matchings. 相似文献
18.
Men's and women's preferences are intercorrelated to the extent that men rank highly those women who rank them highly. Intercorrelation plays an important but overlooked role in determining outcomes of matching mechanisms. We employ simulation techniques to quantify the effects of intercorrelated preferences on men's and women's aggregate satisfaction with the outcome of the Gale–Shapley matching mechanism. Our results show that even a small amount of positive intercorrelation in a matching market means increased satisfaction for women and dramatically decreased potential for strategic manipulation. Negative intercorrelation has the opposite effects. Thus, matching markets characterized by positive intercorrelation are well suited for matching via Gale–Shapley, while markets characterized by negative intercorrelation may face opposition from the nonproposing side of the market. So that our results are immediately applicable, we also define and employ a general measure of intercorrelation that can be used for any matching market. 相似文献
19.
In the many-to-one matching model with contracts, I provide new necessary and new sufficient conditions for the existence of a stable allocation. These new conditions exploit the fact that one side of the market has strict preferences over individual contracts. 相似文献
20.
If agents negotiate openly and form coalitions, can they reach efficient agreements? We address this issue within a class of coalition formation games with externalities where agents’ preferences depend solely on the coalition structure they are associated with. We derive Ray and Vohra's [Equilibrium binding agreements, J. Econ. Theory 73 (1997) 30-78] notion of equilibrium binding agreements using von Neumann and Morgenstern [Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944] abstract stable set and then extend it to allow for arbitrary coalitional deviations (as opposed to nested deviations assumed originally). We show that, while the extended notion facilitates the attainment of efficient agreements, inefficient agreements can nevertheless arise, even if utility transfers are possible. 相似文献