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Assignment games with stable core

Author

Listed:
  • T. E. S. Raghavan

    (Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607, USA Partially funded by NSF Grant DMS 970-4951. Final version: April 1, 2001)

  • Tamás Solymosi

    (Department of Operations Research, Budapest University of Economic Sciences and Public Administration, 1828 Budapest, Pf. 489, Hungary Supported by OTKA Grant T030945.)

Abstract

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.

Suggested Citation

  • T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    • Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:177-185
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