International Journal of Game Theory

, Volume 30, Issue 2, pp 177–185

Assignment games with stable core

  • Tamás Solymosi
  • T. E. S. Raghavan

DOI: 10.1007/s001820100072

Cite this article as:
Solymosi, T. & Raghavan, T. Game Theory (2001) 30: 177. doi:10.1007/s001820100072

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.

Key words: assignment gamestable corelarge coreexact game

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Tamás Solymosi
    • 1
  • T. E. S. Raghavan
    • 2
  1. 1.Department of Operations Research, Budapest University of Economic Sciences and Public Administration, 1828 Budapest, Pf. 489, Hungary (e-mail: tamas.solymosi@opkut.bke.hu.) Supported by OTKA Grant T030945.HU
  2. 2.Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607, USA (e-mail: ter@uic.edu.) Partially funded by NSF Grant DMS 970-4951.US