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The Role Played By Simple Outcomes In Coalition Formation Process Of The Core Outcomes

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  • Marilda Sotomayor

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    Abstract

    In the one-sided Assignment game any two agents can form a partnership. If this is done, the partners undertake some joint activity, which produces a gain that is split between them. We approach this model by focusing on simple outcomes - feasible and individually rational outcomes where only unmatched agents can block. We prove that this blocking can be done in such a way that the payoffs from the trades done are not changed as players reach the core. The core is non-empty iff every simple and unstable outcome can be extended to a simple outcome by a sequence of adjustments in which, at each step, payoffs are preserved for agents already matched and increased only for those newly matching. Hence, starting from the simple outcome where everybody stands alone, we can gradually increase cooperation by making Pareto improvements (and still staying within simple outcomes), until we reach the core, or until the payoff cannot be simple anymore. That is, increase in payoffs is only available through non-optimal cooperation of some agents. In addition, the total sum of these payoffs is the same at any core outcome. The gains in insight with this approach allows a necessary and sufficient condition for the non-emptiness of the core to be identified. Several properties of the core outcomes of economic interest are proved.

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    File URL: http://www.fea.usp.br/feaecon/RePEc/documentos/MarildaSotomayor27WP.pdf
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    Bibliographic Info

    Paper provided by University of São Paulo (FEA-USP) in its series Working Papers, Department of Economics with number 2012_27.

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    Date of creation: 05 Nov 2012
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    Handle: RePEc:spa:wpaper:2012wpecon27

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    Related research

    Keywords: matching; assignment game; core; Pareto optimal simple outcome;

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    1. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, MIT Press, vol. 119(2), pages 457-488, May.
    2. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July.
    3. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
    4. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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