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Stable Matching Games [article]

Felipe Garrido-Lucero, Rida Laraki
2021 arXiv   pre-print
They defined a matching as stable if no unmatched pair can both improve their utility by forming a new pair. They proved, algorithmically, the existence of a stable matching.  ...  We offer a further extension by assuming that matched couples obtain their payoff endogenously as the outcome of a strategic game they have to play in a usual non-cooperative sense (without commitment)  ...  Let Γ be a matching game where all strategic games are zero-sum games with a value. Let π = (µ, x, y) be an externally stable matching and (i, j) be a matched couple.  ... 
arXiv:2008.01680v2 fatcat:rtps6kugibfw3dshrtnpg6yz6e

EPTAS for stable allocations in matching games [article]

Felipe Garrido-Lucero, Rida Laraki
2021 arXiv   pre-print
stable matching (i.e. no uncoupled pair can be better off by matching).  ...  In this paper, we study an extension where matched couples obtain their payoffs as the outcome of a strategic game and more particularly a solution concept that combines Gale-Shapley pairwise stability  ...  and continuous payoff functions, the matching game admits an externally stable matching profile.  ... 
arXiv:2107.07440v2 fatcat:3qpxqfmqmvhcjjsmwqi23s6pzu

Stable Matching Games: Manipulation via Subgraph Isomorphism

Sushmita Gupta, Sanjukta Roy
2017 Algorithmica  
As the name suggests, the men-optimal stable matching is a stable matching that is no worse than any other stable matching, in terms of the preferences of the men.  ...  Gale and Shapley [9] showed that every instance of the Stable Matching problem admits a stable matching.  ...  We complemented this result by showing that unless ETH fails the F S T T C S 2 0 1 6 29:14 Stable Matching Games: Manipulation via Subgraph Isomorphism running time bound is asymptotically optimal.  ... 
doi:10.1007/s00453-017-0382-5 fatcat:txog53msovgvxlpc7mvtw5x67q

Stable Nash Equilibria in the Gale-Shapley Matching Game [article]

Sushmita Gupta and Kazuo Iwama and Shuichi Miyazaki
2015 arXiv   pre-print
In this article we study the stable marriage game induced by the men-proposing Gale-Shapley algorithm.  ...  In this paper, we consider (safe) manipulation that implies a stable matching in a most general setting.  ...  Suppose that the stable matching game is induced by the men-optimal stable matching mechanism.  ... 
arXiv:1509.04344v1 fatcat:7sasexmqznhftoll3bm6owieea

Stable Schedule Matching under Revealed Preference [chapter]

A. Alkan, D. Gale
2003 ICM Millennium Lectures on Games  
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  ...  There exists a stable matching. Proof.  ... 
doi:10.1007/978-3-662-05219-8_1 fatcat:z7dbg2prr5f7zmaq2ojmkqb5ie

Friendship, Altruism, and Reward Sharing in Stable Matching and Contribution Games [article]

Elliot Anshelevich, Onkar Bhardwaj, Martin Hoefer
2012 arXiv   pre-print
We consider the existence, computation, and inefficiency of stable matchings from which no pair of players wants to deviate.  ...  Furthermore, a good stable matching achieving the price of stability bound always exists and can be reached in polynomial time.  ...  Stable Matching and Contribution Games In this paper we consider two classes of games: stable matching with cardinal utilities, and convex contribution games.  ... 
arXiv:1204.5780v1 fatcat:szdcdd7pkzc2jmybcf4d6jease

Finding all stable matchings with couples

Fuhito Kojima
2015 Journal of Dynamics & Games  
In two-sided matching markets in which some doctors form couples, we present an algorithm that finds all the stable matchings whenever one exists, and otherwise shows that there is no stable matching.  ...  Based on that result, an algorithm is presented that finds all the stable matchings, if any, in a market with couples. Journal of Economic Literature Classification Numbers: C78, D71, J01.  ...  However, the stable matchings found by their method may not exhaust the entire set of stable matchings. 5 Indeed, there may be a different stable matching in which welfare of participants is quite different  ... 
doi:10.3934/jdg.2015008 fatcat:mxgmhcfgrfcn5el5vmro5geme4

Route-cost-assignment with joint user and operator behavior as a many-to-one stable matching assignment game

Saeid Rasulkhani, Joseph Y.J. Chow
2019 Transportation Research Part B: Methodological  
The model finds stable pricing, in terms of generalized costs, and matches between user populations in a network to set of routes with line capacities.  ...  We propose a generalized market equilibrium model using assignment game criteria for evaluating transportation systems that consist of both operators' and users' decisions.  ...  Review of assignment games The stable matching problem has a long literature.  ... 
doi:10.1016/j.trb.2019.04.008 fatcat:phfwumdiwbefvphfiifobgjuty

Asymptotically stable matchings and evolutionary dynamics of preference revelation games in marriage problems [article]

Hidemasa Ishii, Nariaki Nishino
2022 arXiv   pre-print
matchings are stable when they exist.  ...  We formulate the asymptotic stability of a matching, indicating the dynamical robustness against sufficiently small changes in players' preference reporting strategies, and show that asymptotically stable  ...  They also showed the existence of the M -optimal stable matching: i.e. a stable matching that is preferred to all the other stable matchings by all men.  ... 
arXiv:2205.08079v1 fatcat:5udvylikdbb2hlmok26qnqslem

Median Stable Matching for College Admissions

Bettina Klaus, Flip Klijn
2006 International Journal of Game Theory  
generalized median stable matchings.  ...  Furthermore, we discuss the fairness properties of median stable matchings and conclude with two illustrative examples of college admissions markets, the lattices of stable matchings, and the corresponding  ...  among all k stable matchings.  ... 
doi:10.1007/s00182-006-0009-6 fatcat:q5kbeqegezbjnciqokwlbxfqwe

Compromises and Rewards: stable and non-manipulable probabilistic matching

Jens Gudmundsson
2018 International Journal of Game Theory  
Randomizing between the W -and the M -optimal stable matching is ex-post stable and weakly ex-post non-manipulable. 10 Specifically, the rule that, for each profile, selects the probabilistic matching  ...  induced by the degenerate lottery that puts probability 1 on the W -optimal stable matching. 11 In consequence, Compromises and Rewards is not ex-post individually rational.  ...  A matching that is not blocked is stable. The set of stable matchings at R is S(R) ⊆ M.  ... 
doi:10.1007/s00182-018-0622-1 fatcat:uywmkbo3njbrdioagtduwtx7ge

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Péter Biró, Tamás Fleiner
2016 Discrete Optimization  
Stable allocation is a general solution concept for games where both the players and their possible cooperations can have capacities.  ...  We show that the problem of finding a stable allocation, given a finitely generated NTU-game with capacities, is always solvable by a variant of Scarf's Lemma.  ...  Fractional stable matching for hypergraphs For a finitely generated NTU-game, the problem of finding a stable outcome is equivalent to the stable matching problem (sm for short) for a hypergraph, as defined  ... 
doi:10.1016/j.disopt.2015.02.002 fatcat:omycadr2ifbhnp7xtbfrr2yiy4

Median stable matchings in two-sided markets

Peter Chen, Michael Egesdal, Marek Pycia, M. Bumin Yenmez
2016 Games and Economic Behavior  
We show that generalized median stable matchings exist in many-to-many matching markets when contracts are strong substitutes and satisfy the law of aggregate demand.  ...  In particular, if there is an odd number k of stable matchings then the median stable matching is the k+1 2 -th best stable matching for all agents on the chosen side.  ...  Moreover, these matchings are aligned in the following way: the worker-optimal stable matching is the firm-pessimal stable matching, the (2)-nd generalized stable matching for workers is the (k − 1)-th  ... 
doi:10.1016/j.geb.2016.03.004 fatcat:ie33kysvvja33owzmvja7oamey

STABLE SOLUTIONS ON MATCHING MODELS WITH QUOTA RESTRICTION

DELFINA FEMENIA, MABEL MARÍ, ALEJANDRO NEME, JORGE OVIEDO
2011 International Game Theory Review  
In this paper, we present a matching market in which an institution has to hire a set of pairs of complementary workers, and has a quota that is the maximum number of candidates pair positions to be ..  ...  the stable sets under responsive restriction of the institution's preference.  ...  as a stable set of standard matching submarket.  ... 
doi:10.1142/s0219198911002927 fatcat:3geovu34dfe43httkju2l6x5si

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

Ayşe Yazıcı
2016 International Journal of Game Theory  
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.  ...  However, each stable match for the true preferences can be achieved as the outcome of such equilibrium.  ...  Therefore, it is crucial to study equilibria of the game induced by a stable matching rule.  ... 
doi:10.1007/s00182-015-0525-3 fatcat:3sl6txnhyjg67pggwvtqucppay
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