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Cycles and Third-Party Payments in the Partnership Formation Problem

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Abstract

We characterize the core of the partnership formation problem (Talman and Yang, Journal of Mathematical Economics 47, 2011) using cycles in the solution of a linear programming problem. The cycles also lead us to a new and intuitive sufficient condition for the existence of equilibrium, generalizing known results. We then introduce the partnership-stable equilibrium, a weakened solution concept in the sense that each equilibrium is also a partnership-stable equilibrium, and find sufficient and necessary conditions for its existence. Finally, we conduct a simulation study to see how often existence is an issue and which factors affect the rate at which problems have solutions.

Suggested Citation

  • Gudmundsson, Jens, 2013. "Cycles and Third-Party Payments in the Partnership Formation Problem," Working Papers 2013:16, Lund University, Department of Economics.
  • Handle: RePEc:hhs:lunewp:2013_016
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    File URL: http://project.nek.lu.se/publications/workpap/papers/WP13_16.pdf
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    1. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    2. Gudmundsson, Jens, 2013. "A Review of the Existence of Stable Roommate Matchings," Working Papers 2013:8, Lund University, Department of Economics.
    3. Andersson, Tommy & Gudmundsson, Jens & Talman, Dolf & Yang, Zaifu, 2014. "A competitive partnership formation process," Games and Economic Behavior, Elsevier, vol. 86(C), pages 165-177.
    4. Johan Karlander & Kimmo Eriksson, 2001. "Stable outcomes of the roommate game with transferable utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 555-569.
    5. Talman, Dolf & Yang, Zaifu, 2011. "A model of partnership formation," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 206-212, March.
    6. Bettina Klaus & Alexandru Nichifor, 2010. "Consistency in one-sided assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 415-433, September.
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    Cited by:

    1. Gudmundsson , Jens, 2014. "Sequences in Pairing Problems: A New Approach to Reconcile Stability with Strategy-Proofness for Elementary Matching Problems," Working Papers 2014:40, Lund University, Department of Economics.
    2. Teytelboym, Alexander, 2014. "Gross substitutes and complements: A simple generalization," Economics Letters, Elsevier, vol. 123(2), pages 135-138.

    More about this item

    Keywords

    Partnership; equilibrium; linear programming; cycles; third-party payments;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D60 - Microeconomics - - Welfare Economics - - - General

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