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On symmetry in the formation of stable partnerships

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Abstract

In this note, we examine the connection between the roommate model and the partnership formation model (Talman and Yang, 2011, Journal of Mathematical Economics 47, 206-212). Upon noting that both occasionally lack equilibria we look at the stable partnerships model, a combination of the former models and interpretable as one with a social planner. We find two sufficient conditions for the existence of stable matchings in the stable partnerships model, where one relates to efficiency, and one (the symmetry condition) to fairness. Finally, we provide examples from the fair sharing literature on dividing common values that satisfy the symmetry condition.

Suggested Citation

  • Gudmundsson, Jens, 2011. "On symmetry in the formation of stable partnerships," Working Papers 2011:29, Lund University, Department of Economics.
  • Handle: RePEc:hhs:lunewp:2011_029
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    File URL: http://project.nek.lu.se/publications/workpap/papers/WP11_29.pdf
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    References listed on IDEAS

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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. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    3. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    4. Alvaro Rodrigues-Neto, Jose, 2007. "Representing roommates' preferences with symmetric utilities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 545-550, July.
    5. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    6. Marilda Sotomayor, 2012. "The Role Played By Simple Outcomes In Coalition Formation Process Of The Core Outcomes," Working Papers, Department of Economics 2012_27, University of São Paulo (FEA-USP).
    7. Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 647-667, October.
    8. 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.
    9. Talman, Dolf & Yang, Zaifu, 2011. "A model of partnership formation," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 206-212, March.
    10. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
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    Keywords

    One-sided matching; partnership formation; symmetry condition; stability;

    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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