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Assignment Games with Externalities

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  • Gudmundsson, Jens
  • Habis, Helga

Abstract

We examine assignment games, wherematched pairs of firms and workers create some monetary value to distribute among themselves and the agents aim to maximize their payoff. In the majority of this literature, externalities - in the sense that a pair’s value depends on the pairing of the others - have been neglected. However, inmost applications a firm’s success depends on, say, the success of its rivals and suppliers. Thus, it is natural to ask how the classical results on assignment games are affected by the introduction of externalities? The answer is – dramatically. We find that (i) a problem may have no stable outcome, (ii) stable outcomes can be inefficient (not maximize total value), (iii) efficient outcomes can be unstable, and (iv) the set of stable outcomes may not form a lattice. We show that stable outcomes always exist if agents are "pessimistic." This is a knife-edge result: there are problems in which the slightest optimism by a single pair erases all stable outcomes.

Suggested Citation

  • Gudmundsson, Jens & Habis, Helga, 2015. "Assignment Games with Externalities," Corvinus Economics Working Papers (CEWP) 2015/16, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2015/16
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    File URL: https://unipub.lib.uni-corvinus.hu/2063/
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    References listed on IDEAS

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    1. Sasaki, Hiroo & Toda, Manabu, 1996. "Two-Sided Matching Problems with Externalities," Journal of Economic Theory, Elsevier, vol. 70(1), pages 93-108, July.
    2. Li, S., 1993. "Compititive Matching Equilibrium and Multiple Principal- Agent Models," Papers 267, Minnesota - Center for Economic Research.
    3. László Kóczy, 2007. "A recursive core for partition function form games," Theory and Decision, Springer, vol. 63(1), pages 41-51, August.
    4. Kimmo Eriksson & Fredrik Jansson & Thomas Vetander, 2011. "The Assignment Game With Negative Externalities And Bounded Rationality," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 443-459.
    5. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 157-171.
    6. Ismail Saglam & Ayse Mumcu, 2007. "The core of a housing market with externalities," Economics Bulletin, AccessEcon, vol. 3(57), pages 1-5.
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    Cited by:

    1. Chen, Bo, 2013. "Assignment Games with Externalities And Matching-Based Cournot Competition," Bonn Econ Discussion Papers 08/2013, University of Bonn, Bonn Graduate School of Economics (BGSE).
    2. Jens Gudmundsson, 2014. "Sequences in Pairing Problems: A new approach to reconcile stability with strategy-proofness for elementary matching problems," 2014 Papers pgu351, Job Market Papers.
    3. Bo Chen, 2019. "Downstream competition and upstream labor market matching," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1055-1085, December.

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    More about this item

    Keywords

    two-sided matching; assignment game; externalities; stability; efficiency;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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