Stability and Price Equilibria in a Many-to-Many Gale-Shapley Market Model

• Autorzy: Zbigniew Świtalski

Warianty tytułu

Stabilność i równowagi cenowe w modelu rynku Gale'a-Shapleya typu "many-to-many"

• Języki publikacji: EN

Abstrakty

EN

In the paper we study relationships between generalized competitive equilibria defined in the paper of Świtalski (2016) and price equilibria for some variant of many-to-many market model of GaleShapley type and between price equilibria and stable matchings for such a model. Obtained results are used for proving theorems on existence of price equilibria in the many-to-many GS-model and in the many-to-many model generalizing the model of Chen, Deng and Ghosh (Chen et al., 2014). (original abstract)

W artykule zbadano zależności między uogólnionymi równowagami konkurencyjnymi zdefiniowanymi w pracy Świtalskiego (2016), a równowagami cenowymi dla pewnego wariantu modelu rynku Gale'a-Shapleya (typu "many-to-many"), a także między równowagami cenowymi a skojarzeniami stabilnymi dla tego modelu. Uzyskane wyniki wykorzystano do udowodnienia twierdzeń o istnieniu równowag cenowych w modelu GS typu many-to-many oraz w pewnym modelu typu many-to-many uogólniającym model zawarty w pracy Chen i inni (2014). (abstrakt oryginalny)

Słowa kluczowe

EN

Price competition; Mathematical economic models; Mathematical economics; Market equilibrium

PL

Konkurencja cenowa; Matematyczne modele ekonomiczne; Ekonomia matematyczna; Równowaga rynkowa

• Czasopismo: Przegląd Statystyczny
• Rocznik: 2017
• Tom: 64
• Numer: z. 3
• Strony: 229--248

Twórcy

autor

Zbigniew Świtalski

• University of Zielona Góra

Bibliografia

• Aizerman M., Aleskerov F., (1995), Theory of Choice, North-Holland, Amsterdam.
• Aleskerov F., Monjardet B., (2002), Utility Maximization, Choice and Preference, Springer, Berlin.
• Alkan A., Gale D., (2003), Stable Schedule Matching under Revealed Preference, Journal of Economic Theory, 112, 289-306.
• Andersson T., Erlanson A., (2013), Multi-item Vickrey-English-Dutch Auctions, Games and Economic Behavior, 81, 116-129.
• Azevedo E. M., Leshno J. D., (2011), A Supply and Demand Framework for Two-sided Matching Markets, working paper, www.aeaweb.org (last access: 28.07.2016).
• Biro P., Kiselgof S., (2013), College Admissions with Stable Score-Limits, discussion paper, Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences, Budapest.
• Camina E., (2006), A Generalized Assignment Game. Mathematical Social Sciences, 52, 152-161.
• Chen N., Deng X., Ghosh A., (2014), Competitive Equilibria in Matching Markets with Budgets, www. arxiv.org (last access: 28.07.2016).
• Crawford V. P., Knoer E. M., (1981), Job Matching with Heterogeneous Firms and Workers, Econometrica, 49, 437-450.
• Danilov V., Koshevoy G., (2005), Mathematics of Plott Choice Functions, Mathematical Social Sciences, 49, 245-272.
• Echenique F., (2007), Counting Combinatorial Choice Rules, Games and Economic Behavior, 58, 231-245.
• Echenique F., Oviedo J., (2006), A Theory of Stability in Many-to-Many Matching Markets, Theoretical Economics, 1, 233-273.
• Gale D., (1960), The Theory of Linear Economic Models, The University of Chicago Press, Chicago.
• Gale D., Shapley L. S., (1962), College Admissions and the Stability of Marriage, American Mathematical Monthly, 69, 9-15.
• Hatfield J. W., Kominers S. D., (2016) Contract Design and Stability in Many-to-Many Matching, Games and Economic Behavior (in press).
• Hatfield J. W., Kominers S. D., Nichifor A., Ostrovsky M., Westkamp A., (2013), Stability and Competitive Equilibrium in Trading Networks, Journal of Political Economy, 121 (5), 966-1005.
• Herings P. J., (2015), Equilibrium and Matching under Price Control, working paper RM/15/001, Maastricht University, Graduate School of Business and Economics.
• Klaus B., Walzl M., (2009), Stable Many-to-Many Matchings with Contracts, Journal of Mathematical Economics, 45, 422-434.
• Kominers S. D., (2012), On the Correspondence of Contracts to Salaries in (Many-to-Many) Matching, Games and Economic Behavior, 75, 984-989.
• Roth A. E., (2002), The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics, Econometrica, 70, 1341-1378.
• Roth A. E., Sotomayor M. A., (1992), Two-Sided Matching. A Study in Game-Theoretic Modeling and Analysis, Cambridge University Press.
• Shapley L. S., Shubik M., (1971/72), The Assignment Game I: The Core, International Journal of Game Theory, 1, 111-130.
• Sönmez T., Ünver M. U., (2011), Matching, Allocation and Exchange of Discrete Resources, in: Benhabib J., Bisin A., Jackson M. O., (eds.), Handbook of Social Economics, 781-852.
• Sotomayor M., (2007), Connecting the Cooperative and Competitive Structures of the Multiple Partners Assignment Game, Journal of Economic Theory, 134, 155-174.
• Świtalski Z., (2008), Stability and Equilibria in the Matching Models, Scientific Research of the Institute of Mathematics and Computer Science, Częstochowa University of Technology, 2 (7), 77-85.
• Świtalski Z., (2010), Equilibria in Markets with Two-Sided Preferences (in Polish), Przegląd Statystyczny, 4 (57), 54-69.
• Świtalski Z., (2015), Some Properties of Competitive Equilibria and Stable Matchings in a Gale-Shapley Market Model, Studia Ekonomiczne, Scientific Papers of the University of Economics, Katowice, 248, 222-232.
• Świtalski Z., (2016), Stability and Generalized Competitive Equilibria in a Many-to-Many Gale-Shapley Market Model, Przegląd Statystyczny, 3 (63), 237-253.