We characterize the assignment games which admit a population monotonic allocation scheme (PMAS) in terms of efficiently verifiable structural properties of the nonnegative matrix that induces the game. We prove that an assignment game is PMAS-admissible if and only if the positive elements of the underlying nonnegative matrix form orthogonal submatrices of three special types. In game theoretic terms it means that an assignment game is PMAS-admissible if and only if it contains either a veto player or a dominant veto mixed pair, or the game is a composition of these two types of special assignment games. We also show that in PMAS-admissible assignment games all core allocations can be extended to a PMAS, and the nucleolus coincides with the tau-value.

我们根据引发博弈的非负矩阵的可有效验证的结构特性来描述分配博弈，该博弈承认群体单调分配方案（PMAS）。我们证明，当且仅当基础非负矩阵的正元素形成三种特殊类型的正交子矩阵时，分配游戏才是 PMAS 可接受的。用博弈论术语来说，这意味着分配博弈是 PMAS 可接受的，当且仅当它包含否决玩家或占主导地位的否决混合对，或者博弈是这两种类型的特殊分配博弈的组合。我们还表明，在 PMAS 允许的分配游戏中，所有核心分配都可以扩展到 PMAS，并且核仁与 tau 值一致。