A 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 also implies that whether a matching game admits population monotonic allocation schemes can be determined efficiently.

翻译：匹配游戏是一种合作赢利游戏,其定义在边加权图中,玩家是脊椎,联盟的利润是联盟引领的地盘中匹配的最大权重。人口单调分配计划是一系列规则,规定如何在每个联盟的玩家之间分享利润,这样当联盟扩大时,每个玩家都得到更好的对待。在本文中,我们研究匹配游戏,为人口单调分配计划的存在提供必要和充分的定性。我们的定性还意味着匹配游戏能否有效地确定人口单调分配计划。