2022/10/31 by Tamás Solymosi, Solymosi, Tamás
Computer Science · #91A12 #91A43 #91B68 #Bayesian Modeling and Causal Inference #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Economics and business #J.4 #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2210.17373
openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.