International Journal of Game Theory

, Volume 30, Issue 2, pp 177-185

First online:

Assignment games with stable core

  • Tamás SolymosiAffiliated withDepartment of Operations Research, Budapest University of Economic Sciences and Public Administration, 1828 Budapest, Pf. 489, Hungary (e-mail: Supported by OTKA Grant T030945.
  • , T. E. S. RaghavanAffiliated withDepartment of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607, USA (e-mail: Partially funded by NSF Grant DMS 970-4951.

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We prove that the core of an assignment game (a two-sided matching game with transferable utility as introduced by Shapley and Shubik, 1972) 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 aformentioned conditions.

Key words: assignment game stable core large core exact game