Abstract
Starting with two models fifty years ago, the discrete marriage game [1] and the continuous assignment game [2], the study of stable matchings has evolved into a rich theory with applications in many areas. Most notably, it has lead to a number of truthful mechanisms that have seen a recent rejuvenation in the context of sponsored search. In this paper we survey the history of these problems and provide several links to ongoing research in the field.
This work was conducted as part of a EURYI scheme award (see http://www.esf.org/euryi/ ).
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References
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. The American Mathematical Monthly 69(1), 9–15 (1962)
Shapley, L., Shubik, M.: The assignment game I: The core. International Journal of Game Theory 1(2), 111–130 (1972)
Myerson, R.B.: Game Theory: Analysis of Conflict. Harvard University Press, Cambridge (1997)
Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)
Dubins, L.E., Freedman, D.A.: Ms. Machiavelli and the Gale-Shapley algorithm. American Mathematical Monthly 88(7), 485–494 (1981)
Demange, G., Sotomayor, M.A.O.: Some remarks on the stable matching problem. Discrete Applied Mathematics 11(3), 223–232 (1985)
Roth, A.E., Sotomayor, M.A.O.: Two-Sided Matching - A Study in Game-Theoretic Modelling and Analysis. Cambridge University Press, Cambridge (1990)
Manlove, D.F., Irving, R.W., Iwama, K., Miyazaki, S., Morita, Y.: Hard variants of stable marriage. Theoretical Computer Science 276(1-2), 261–279 (2002)
Leonard, H.B.: Elicitation of honest preferences for the assignment of individuals to positions. The Journal of Political Economy 91(3), 461–479 (1983)
Demange, G., Gale, D., Sotomayor, M.A.O.: Multi-item auctions. The Journal of Political Economy 94(4), 863–872 (1986)
Kuhn, H.: The Hungarian Method for the assignment problem. Naval Research Logistics Quarterly 2(1-2), 83–97 (1955)
Frank, A.: On Kuhn’s Hungarian Method - A tribute from Hungary. Naval Research Logistics 51(1), 2–5 (2004)
Hall, P.: On representatives of subsets. J. London Math. Soc. 10(2), 26–30 (1935)
Aggarwal, G., Muthukrishna, S., Pál, D., Pál, M.: General auction mechanism for search advertising. In: World Wide Web Conference, pp. 241–250 (2009)
Dütting, P., Henzinger, M., Weber, I.: Sponsored search, market equilibria, and the Hungarian Method. In: Symposium on Theoretical Aspects of Computer Science, pp. 287–298 (2010)
Alkan, A.: Existence and computation of matching equilibria. European Journal of Political Economy 5(2-3), 285–296 (1989)
Alkan, A.: Equilibrium in a Matching Market with General Preferences. In: Equilibrium and Dynamics. Essays in Honour of David Gale, The MacMillan Press Ltd., Basingstoke (1992)
Demange, G., Gale, D.: The strategy structue of two-sided matching markets. Econometrica 53(4), 873–883 (1985)
Dütting, P., Henzinger, M., Weber, I.: Bidder optimal assignments for general utilities. In: Workshop on Internet and Network Economics, pp. 575–582 (2009)
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Dütting, P., Henzinger, M. (2010). Mechanisms for the Marriage and the Assignment Game. In: Calamoneri, T., Diaz, J. (eds) Algorithms and Complexity. CIAC 2010. Lecture Notes in Computer Science, vol 6078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13073-1_2
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