Assignment games with stable core

Assignment games with stable core

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Article ID: iaor2003663
Country: Germany
Volume: 30
Issue: 2
Start Page Number: 177
End Page Number: 185
Publication Date: Jan 2001
Journal: International Journal of Game Theory
Authors: ,
Abstract:

We prove that the core of an assignment game (a two-sided matching game with transferable utility as introduced by Shapley and Shubik) is stable (i.e., it is the unique von Neumann–Morgenstern solution) if and only if there is a matching between the two types of players such that the corresponding entries in the underlying matrix are all row and column maximums. We identify other easily verifiable matrix properties and show their equivalence to various known sufficient conditions for core-stability. By these matrix characterizations we found that on the class of assignment games, largeness of the core, extendability and exactness of the game are all equivalent conditions, and strictly imply the stability of the core. In turn, convexity and subconvexity are equivalent, and strictly imply all aforementioned conditions.

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