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 Gale- Shapley 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).
stable matching, Gale-Shapley theory, many-to-many model, price equilibrium, choice function, discrete market model
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.