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Population monotonicity in matching games

Author

Listed:
  • Han Xiao

    (Ocean University of China)

  • Qizhi Fang

    (Ocean University of China)

Abstract

The matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population monotonic allocation scheme is a collection of rules defining how to share the profit among players in each coalition such that every player is better off when the coalition expands. In this paper, we study matching games and provide a necessary and sufficient characterization for the existence of population monotonic allocation schemes. Our characterization implies that whether a matching game admits population monotonic allocation schemes can be determined efficiently.

Suggested Citation

  • Han Xiao & Qizhi Fang, 2022. "Population monotonicity in matching games," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 699-709, May.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:4:d:10.1007_s10878-021-00804-3
    DOI: 10.1007/s10878-021-00804-3
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    References listed on IDEAS

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    More about this item

    Keywords

    Cooperative game theory; Matching game; Population monotonic allocation scheme;
    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

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