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Population monotonicity in matching games

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.

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Acknowledgements

We appreciate two anonymous referees for their helpful comments and valuable suggestions which greatly improved the presentation of this work.

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Correspondence to Han Xiao.

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Supported in part by the National Natural Science Foundation of China (Nos. 12001507, 11971447, 11871442) and the Natural Science Foundation of Shandong (No. ZR2020QA024).

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Xiao, H., Fang, Q. Population monotonicity in matching games. J Comb Optim (2021). https://doi.org/10.1007/s10878-021-00804-3

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Keywords

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

Mathematics Subject Classification

  • 05C57
  • 91A12
  • 91A43
  • 91A46

JEL Classification

  • C71
  • C78