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Equilibria of two-sided matching games with common preferences

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  • Alpern, Steve
  • Katrantzi, Ioanna

Abstract

Problems of matching have long been studied in the operations research literature (assignment problem, secretary problem, stable marriage problem). All of these consider a centralized mechanism whereby a single decision maker chooses a complete matching which optimizes some criterion. This paper analyzes a more realistic scenario in which members of the two groups (buyers-sellers, employers-workers, males-females) randomly meet each other in pairs (interviews, dates) over time and form couples if there is mutual agreement to do so. We assume members of each group have common preferences over members of the other group. Generalizing an earlier model of Alpern and Reyniers [Alpern, S., Reyniers, D.J., 2005. Strategic mating with common preferences. J. Theor. Biol. 237, 337-354], we assume that one group (called males) is r times larger than the other, r[greater-or-equal, slanted]1. Thus all females, but only 1/r of the males, end up matched. Unmatched males have negative utility -c. We analyze equilibria of this matching game, depending on the parameters r and c. In a region of (r,c) space with multiple equilibria, we compare these, and analyze their 'efficiency' in several respects. This analysis should prove useful for designers of matching mechanisms who have some control over the sex ratio (e.g. by capping numbers of males at a 'singles event'or by having 'ladies free' nights) or the nonmating cost c (e.g. tax benefits to married couples).

Suggested Citation

  • Alpern, Steve & Katrantzi, Ioanna, 2009. "Equilibria of two-sided matching games with common preferences," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1214-1222, August.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:3:p:1214-1222
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    References listed on IDEAS

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    1. Bloch, Francis & Ryder, Harl, 2000. "Two-Sided Search, Marriages, and Matchmakers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 93-115, February.
    2. Shmuel Gal, 1999. "Rendezvous Search on the Line," Operations Research, INFORMS, vol. 47(6), pages 974-976, December.
    3. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
    4. Steve Alpern, 2002. "Rendezvous Search: A Personal Perspective," Operations Research, INFORMS, vol. 50(5), pages 772-795, October.
    5. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    6. Ken Burdett & Melvyn G. Coles, 1997. "Marriage and Class," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(1), pages 141-168.
    7. Edmund J. Collins & John M. McNamara & David M. Ramsey, 2006. "Learning rules for optimal selection in a varying environment: mate choice revisited," Behavioral Ecology, International Society for Behavioral Ecology, vol. 17(5), pages 799-809, September.
    8. Burdett, Kenneth & Coles, Melvyn G, 1999. "Long-Term Partnership Formation: Marriage and Employment," Economic Journal, Royal Economic Society, vol. 109(456), pages 307-334, June.
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    Cited by:

    1. Alpern, Steve & Katrantzi, Ioanna & Ramsey, David, 2014. "Equilibrium population dynamics when mating is by mutual choice based on age," Theoretical Population Biology, Elsevier, vol. 94(C), pages 63-72.
    2. Biró, Péter & Gudmundsson, Jens, 2021. "Complexity of finding Pareto-efficient allocations of highest welfare," European Journal of Operational Research, Elsevier, vol. 291(2), pages 614-628.
    3. Kong, Qianqian & Peters, Hans, 2023. "Power indices for networks, with applications to matching markets," European Journal of Operational Research, Elsevier, vol. 306(1), pages 448-456.
    4. Alpern, S. & Katrantzi, I. & Ramsey, D.M., 2013. "Partnership formation with age-dependent preferences," European Journal of Operational Research, Elsevier, vol. 225(1), pages 91-99.
    5. Tadeas Priklopil & Krishnendu Chatterjee, 2015. "Evolution of Decisions in Population Games with Sequentially Searching Individuals," Games, MDPI, vol. 6(4), pages 1-25, September.

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