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- Title
Assignment games with population monotonic allocation schemes.
- Authors
Solymosi, Tamás
- Abstract
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.
- Subjects
NONNEGATIVE matrices; GAMES; NUCLEOLUS
- Publication
Social Choice & Welfare, 2024, Vol 62, Issue 1, p67
- ISSN
0176-1714
- Publication type
Article
- DOI
10.1007/s00355-023-01477-z