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The even split rule in positive assortative matching

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  • Jia, Hao

Abstract

Many economic models, especially in two-sided matching literature, involve breaking down a supermodular function into two supermodular functions according to a certain allocation rule. The conventional wisdom is to invoke the Nash bargaining solution, which boils down to an even split rule within the transferable utility framework. This paper rationalizes the use of the Nash bargaining solution in a two-sided matching model by showing that the even split rule is the only allocation which allows the net benefit functions to inherit supermodularity from the joint surplus function, which is necessary to ensure positive assortative matching.

Suggested Citation

  • Jia, Hao, 2019. "The even split rule in positive assortative matching," Journal of Mathematical Economics, Elsevier, vol. 81(C), pages 57-61.
    • Handle: RePEc:eee:mateco:v:81:y:2019:i:c:p:57-61
    DOI: 10.1016/j.jmateco.2019.01.001
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    1. Jeremy Lise & Costas Meghir & Jean-Marc Robin, 2016. "Matching, Sorting and Wages," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 19, pages 63-87, January.
    2. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    3. repec:hal:spmain:info:hdl:2441/78hlmdbud88hhp5vbdddivv2hu is not listed on IDEAS
    4. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    5. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    7. Jan Eeckhout & Philipp Kircher, 2010. "Sorting and Decentralized Price Competition," Econometrica, Econometric Society, vol. 78(2), pages 539-574, March.
    8. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    9. Alp E. Atakan, 2006. "Assortative Matching with Explicit Search Costs," Econometrica, Econometric Society, vol. 74(3), pages 667-680, May.
    10. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    11. Hector Chade & Jan Eeckhout & Lones Smith, 2017. "Sorting through Search and Matching Models in Economics," Journal of Economic Literature, American Economic Association, vol. 55(2), pages 493-544, June.
    12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    13. Lones Smith, 2006. "The Marriage Model with Search Frictions," Journal of Political Economy, University of Chicago Press, vol. 114(6), pages 1124-1146, December.
    14. McFadden, Daniel, 1974. "The measurement of urban travel demand," Journal of Public Economics, Elsevier, vol. 3(4), pages 303-328, November.
    15. Becker, Gary S, 1974. "A Theory of Marriage: Part II," Journal of Political Economy, University of Chicago Press, vol. 82(2), pages 11-26, Part II, .
    16. Gary S. Becker, 1974. "A Theory of Marriage," NBER Chapters, in: Economics of the Family: Marriage, Children, and Human Capital, pages 299-351, National Bureau of Economic Research, Inc.
    17. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    18. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
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    Cited by:

    1. Jia, Hao, 2020. "The even split rule for (concave) symmetric supermodular functions," Economics Letters, Elsevier, vol. 186(C).

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