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.

匹配博弈是定义在边加权图上的合作利润博弈，其中参与者是顶点，联盟的利润是联盟在子图中引起的匹配的最大权重。人口单调分配方案是一组规则，定义了如何在每个联盟中的参与者之间分享利润，以便在联盟扩大时每个参与者的状况都更好。在本文中，我们研究了匹配博弈，并为人口单调分配方案的存在提供了必要和充分的表征。我们的表征意味着匹配游戏是否承认可以有效地确定人口单调分配方案。