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Non-cooperative matching games

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Abstract

Consider a market in which two distinct groups of agents face each other. Every agent can improve upon his status quo if he is matched with a member of the opposite group and if he agrees with his partner how to split the realized gain. The paper presents two non-cooperative games in which the agents construct the allocation without the help of an auctioneer. In the first game the set of equilibria coincides with the cooperative “stable solutions” which are well-established in this context. In the second game it is shown that a change of the order of the moves is sufficient to arrive at a unique equilibrium payoff.

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References

  • Crawford V, Knoer E (1981) Job Matching with Heterogeneous Firms and Workers. Econometrica, Vol. 49, No. 2, pp. 437–450

    Google Scholar 

  • Demange G, Gale D (1985) The Strategy Structure of Two-Sided Matching Markets. Econometrica, Vol. 53, No. 4, pp. 873–888

    Google Scholar 

  • Gale D, Shapley L (1962) College Admissions and the Stability of Marriage. American Mathematical Monthly, Vol. 69, pp. 9–15

    Google Scholar 

  • Kamecke U (1988a) Modelling Competition in Matching Markets with Non-Cooperative Game Theory. Dissertation, University of Bonn

  • Kamecke U (1988b) Computing Equilibrium in a Matching Market with a Walrasian Mechanism. Discussion Paper No. A-208, University of Bonn

  • Kaneko M (1982) The Central Assignment Game and the Assignment Markets. Journal of Mathematical Economics, Vol. 10, No. 2/3, pp. 205–232

    Google Scholar 

  • Nash J (1950) The Bargaining Problem. Econometrica, Vol. 18, No. 1, pp. 155–162

    Google Scholar 

  • Nash J (1951) Non-Cooperative Games. Annals of Mathematics, Vol. 54, No. 2, pp. 286–295

    Google Scholar 

  • Nash J (1953) Two-Person Cooperativ games. Econometrica, Vol. 21, No. 1, pp. 128–140

    Google Scholar 

  • Rochford S (1984) Symmetrically Pairwise-Bargained Allocations in an Assignment Market. Journal of Economic Theory, Vol. 34, No. 2, pp. 262–281

    Google Scholar 

  • Roth A (1979) Axiomatic Models of Bargaining. Lecture Notes in Economics and Mathematical Systems, No. 170 Berlin

  • Roth A (1984a) Stability and Polarization of Interests in Job Matching. Econometrica, Vol. 52, No. 1, pp. 47–57

    Google Scholar 

  • Roth A (1984b) Misrepresentation and Stability in the Marriage Problem. Journal of Economic Theory, Vol. 34, No. 2, pp. 383–387

    Google Scholar 

  • Roth A (1985) The College Admission Problem is not Equivalent to the Marriage Problem. Journal of Economic Theory, Vol. 36, No. 2, pp. 277–288

    Google Scholar 

  • Rubinstein A, Wolinsky A (1985) Equilibrium in a Market with Sequential Bargaining. Econometrica, Vol. 53, No. 5, pp. 1133–1150

    Google Scholar 

  • Shubik M (1984) A Game-Theoretic Approach to Political Economy. London

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Kamecke, U. Non-cooperative matching games. Int J Game Theory 18, 423–431 (1989). https://doi.org/10.1007/BF01358802

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  • DOI: https://doi.org/10.1007/BF01358802

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