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 a veto player or a dominant veto mixed pair or is composed of from these two types of special assignment games. We also show that in a PMAS-admissible assignment game all core allocations can be extended to a PMAS, and the nucleolus coincides with the tau-value.
翻译:我们把允许人口单一分配办法(PMAS)的派任游戏定性为吸引游戏的非消极矩阵的有效可核实结构属性;我们证明,只有以下三种特殊类型非消极矩阵形式正本元素,派任游戏才允许进行派任游戏;在游戏理论术语中,它意味着派任游戏只有在拥有否决权的玩家或具有支配地位的混合否决权或由这两类特殊派任游戏组成的情况下,才允许进行派任游戏;我们还证明,在派任游戏中,所有核心分配可以扩大到PMAS,而核核核核素与Tau值相吻合。