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Monotonic core allocation paths for assignment games

Author

Listed:
  • Takaaki Abe

    (Waseda University)

  • Shuige Liu

    (Waseda University
    Maastricht University)

Abstract

We introduce a modification of Sprumont (Games Econ Behav 2:378–394, 1990) population monotonic allocation scheme (PMAS), called monotonic core allocation path (MCAP) for assignment games, which is a sequence of allocations along an order on the set of players satisfying that (1) each allocation is in the core of the subgame of the corresponding players at that step, and (2) the payoffs for each player are non-decreasing through the sequence. The notion of MCAP preserves the population monotonicity of PMAS while avoids the difficulty that PMAS does not exist in many market games. We show that for every assignment game, there is an order of players along which a MCAP exists. The terminals of MCAP form a refinement of the core. We also show that the terminals of MCAP coincide with the extreme core allocations in two subclasses of assignment games: gloves games and Böhm-Bawerk games. The strong connection of MCAP with extreme core allocations suggests some conflict between the stability of a coalition formation process and the fairness of the resulting outcomes.

Suggested Citation

  • Takaaki Abe & Shuige Liu, 2019. "Monotonic core allocation paths for assignment games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 557-573, December.
    • Handle: RePEc:spr:sochwe:v:53:y:2019:i:4:d:10.1007_s00355-019-01197-3
    DOI: 10.1007/s00355-019-01197-3
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    1. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    2. Josep Izquierdo & Marina Núñez & Carles Rafels, 2007. "A simple procedure to obtain the extreme core allocations of an assignment market," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 17-26, September.
    3. Ortega, Josué, 2018. "Social integration in two-sided matching markets," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 119-126.
    4. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    5. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Pere Villar, Joan, 2002. "Assignment Games Satisfy the CoMa-Property," Games and Economic Behavior, Elsevier, vol. 38(2), pages 231-239, February.
    6. O. Tejada & M. Álvarez-Mozos, 2016. "Vertical syndication-proof competitive prices in multilateral assignment markets," Review of Economic Design, Springer;Society for Economic Design, vol. 20(4), pages 289-327, December.
    7. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
    8. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    9. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    10. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    11. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    12. Manabu Toda, 2006. "Monotonicity and Consistency in Matching Markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 13-31, April.
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