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Axioms for the optimal stable rules and fair-division rules in a multiple-partners job market

Author

Listed:
  • Gerard Domènech Gironell

    (Universitat de Barcelona)

  • Marina Núñez Oliva

    (Universitat de Barcelona)

Abstract

In the multiple-partners job market, introduced in (Sotomayor, 1992), each firm can hire several workers and each worker can be hired by several firms, up to a given quota. We show that, in contrast to what happens in the simple assignment game, in this extension, the firms-optimal stable rules are neither valuation monotonic nor pairwise monotonic. However, we show that the firms-optimal stable rules satisfy a weaker property, what we call firmcovariance, and that this property characterizes these rules among all stable rules. This property allows us to shed some light on how firms can (and cannot) manipulate the firms-optimal stable rules. In particular, we show that firms cannot manipulate them by constantly over-reporting their valuations. Analogous results hold when focusing on the workers. Finally, we extend to the multiple-partners market a known characterization of the fair-division rules on the domain of simple assignment games.

Suggested Citation

  • Gerard Domènech Gironell & Marina Núñez Oliva, 2022. "Axioms for the optimal stable rules and fair-division rules in a multiple-partners job market," UB School of Economics Working Papers 2022/419, University of Barcelona School of Economics.
    • Handle: RePEc:ewp:wpaper:419web
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    File URL: http://hdl.handle.net/2445/185052
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    References listed on IDEAS

    as
    1. Guillermo Owen, 1992. "The Assignment Game : The Reduced Game," Annals of Economics and Statistics, GENES, issue 25-26, pages 71-79.
    2. Kagel, John H & Levin, Dan, 1993. "Independent Private Value Auctions: Bidder Behaviour in First-, Second- and Third-Price Auctions with Varying Numbers of Bidders," Economic Journal, Royal Economic Society, vol. 103(419), pages 868-879, July.
    3. repec:adr:anecst:y:1992:i:25-26:p:03 is not listed on IDEAS
    4. Pérez-Castrillo, David & Sotomayor, Marilda, 2019. "Comparative statics in the multiple-partners assignment game," Games and Economic Behavior, Elsevier, vol. 114(C), pages 177-192.
    5. van den Brink, René & Núñez, Marina & Robles, Francisco, 2021. "Valuation monotonicity, fairness and stability in assignment problems," Journal of Economic Theory, Elsevier, vol. 195(C).
    6. Mamoru Kaneko, 1976. "On the core and competitive equilibria of a market with indivisible goods," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(2), pages 321-337, June.
    7. Kagel, John H. & Lien, Yuanchuan & Milgrom, Paul, 2014. "Ascending prices and package bidding: Further experimental analysis," Games and Economic Behavior, Elsevier, vol. 85(C), pages 210-231.
    8. Marilda Sotomayor, 1992. "The Multiple Partners Game," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 17, pages 322-354, Palgrave Macmillan.
    9. David Pérez-Castrillo & Marilda Sotomayor, 2017. "On the manipulability of competitive equilibrium rules in many-to-many buyer–seller markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1137-1161, November.
    10. Fagebaume, Alexis & Gale, David & Sotomayor, Marilda, 2010. "A note on the multiple partners assignment game," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 388-392, July.
    11. Kagel, John H. & Levin, Dan, 2009. "Implementing efficient multi-object auction institutions: An experimental study of the performance of boundedly rational agents," Games and Economic Behavior, Elsevier, vol. 66(1), pages 221-237, May.
    12. Sotomayor, Marilda, 2007. "Connecting the cooperative and competitive structures of the multiple-partners assignment game," Journal of Economic Theory, Elsevier, vol. 134(1), pages 155-174, May.
    13. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    14. Marilda Sotomayor, 2009. "Adjusting prices in the multiple-partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 575-600, November.
    15. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 567-583.
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    More about this item

    Keywords

    Assignment game; stable rules; fair division.;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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