How game theory enhances life: an introduction to stable matching theory and its applications

Document Type : Research Paper

Authors

1 Imam Sadiq University

2 Allameh Tabataba'i University

3 University of Tehran

Abstract

The joint awarding of the Nobel Prize in Economics in 2012 to a mathematician and an economist signaled a recognition of the importance of game theory and matching models. Matching theory, and the broader field known as market design, are deeply rooted in game theory. The aim of this article is to contribute to the collaborative efforts of mathematicians, economists, and operations researchers in identifying, generalizing, applying mathematical models and game theory. Based on this premise, this article presents a framework for matching theory, explains the theoretical mechanisms of allocation, describes interdisciplinary approaches in this field and illustrates how it is applied to real-life problems.

Keywords

References

[1] J. von Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton University Press, Princeton, 1944.
[2] L. Lovász and M. D. Plummer, Matching theory, North-Holland Mathematics Studies, North-Holland Publishing Co., Ams-terdam; Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1986.
[3] D. Gale and L. S. Shapley, College admissions and the stability of marriage, Amer. Math. Monthly, 69 no. 1 (1962) 9–15.
[4] JSTOR, JSTOR All-Stars: The American Mathematical Monthly, available at
http://www.maa.org/publications/periodicals/american-mathematical-monthly/jstor-all-stars-american-mathematical-monthly (accessed on April 30, 2014).
[5] A. E. Roth and M. Sotomayor, Two-sided matching, A study in game-theoretic modeling and analysis, Cambridge University Press, Cambridge [England], New York, 1990.
[6] D. G. McVitie and L. B. Wilson, Stable marriage assignment for unequal sets, BIT Numerical Mathematics, 10 no. 3 (1970) 295–309.
[7] A. E. Roth, Deferred acceptance algorithms: history, theory, practice, and open questions, Internat. J. Game Theory, 36 no. 3-4 (2008) 537–569.
[8] A. E. Roth, The Economics of Matching: Stability and Incentives, Math. Oper. Res., 7 no. 4 (1982) 617–628.
[9] A. E. Roth, Incentive compatibility in a market with indivisible goods, Econom. Lett., 9 no. 2 (1982) 127–132.
[10] L. E. Dubins and D. A. Freedman, Machiavelli and the Gale-Shapley Algorithm, Amer. Math. Monthly, 88 no. 7 (1981) 485–494.
[11] L. Shapley and H. Scarf, On cores and indivisibility, J. Math. Econom. , 1 no. 1 (1974) 23–37.
[12] D. B. Gillies, Solutions to general non-zero-sum games, in: A. Tucker, R. D. Luce (Eds.), Contributions to the theory of games, Princeton University Press, Princeton, N.J., 1959 47–85.
[13] A. E. Roth and A. Postlewaite, Weak versus strong domination in a market with indivisible goods, J. Math. Econom., 4 no. 2 (1977) 131–137.
[14] A. E. Roth, T. Sönmez and M. U. Ünver, Kidney Exchange, The Quarterly Journal of Economics, 125 no. 2 (2004) 457–488.
[15] A. E. Roth, T. Sönmez and M. U. Ünver, Pairwise kidney exchange, J. Econom. Theory, 125 no. 2 (2005) 151–188.
[16] M. Yakutchik, The Matchmakers.
[17] A. E. Roth, T. Sönmez and M. U. Ünver, Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences, American Economic Review, 97 no. 3 (2007) 828–851.
[18] A. E. Roth, The Evolution of the Labor Market for Medical Interns and Residents: a Case Study in Game Theory, Journal of Political Economy, 92 no. 6 (1984) 991–1016.
[19] A. E. Roth and E. Peranson, The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design, American Economic Review, 89 no. 4 (1999) 748–780.
[20] B. Aldershof and O. M. Carducci, Stable matchings with couples, Discrete Appl. Math., 68 no. 1-2 (1996) 203–207.
[21] A. E. Roth and J. H. V. Vate, Random Paths to Stability in Two-Sided Matching, Econometrica, 58 no. 6 (1990) 1475–1480.
[22] F. Kojima, P. A. Pathak and A. E. Roth, Matching with Couples: Stability and Incentives in Large Markets, National Bureau of Economic Research Working Paper Series No. 16028, 2010.
[23] A. E. Roth, A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom, The American Economic Review, 81 no. 3 (1991) 415–440.
[24] J. Ma, T. Sjöstróm, Matching in Marriage and Markets, Eur. Math. Soc. Newsl., no. 89 (2013) 31–35.

Files

History

  • Receive Date: 26 July 2014
  • Revise Date: 13 February 2016
  • Accept Date: 19 April 2016
  • Publish Date: 22 May 2017

Share

How to cite

Statistics