International Journal of Game Theory

, Volume 1, Issue 1, pp 111–130 | Cite as

The assignment game I: The core

  • L. S. Shapley
  • M. Shubik


The assignment game is a model for a two-sided market in which a product that comes in large, indivisible units (e.g., houses, cars, etc.) is exchanged for money, and in which each participant either supplies or demands exactly one unit. The units need not be alike, and the same unit may have different values to different participants. It is shown here that the outcomes in thecore of such a game — i.e., those that cannot be improved upon by any subset of players — are the solutions of a certain linear programming problem dual to the optimal assignment problem, and that these outcomes correspond exactly to the price-lists that competitively balance supply and demand. The geometric structure of the core is then described and interpreted in economic terms, with explicit attention given to the special case (familiar in the classic literature) in which there is no product differentiation — i.e., in which the units are interchangeable. Finally, a critique of the core solution reveals an insensitivity to some of the bargaining possibilities inherent in the situation, and indicates that further analysis would be desirable using other game-theoretic solution concepts.


Economic Theory Game Theory Programming Problem Product Differentiation Geometric Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Physica-Verlag 1971

Authors and Affiliations

  • L. S. Shapley
    • 1
  • M. Shubik
    • 2
  1. 1.The Rand CorporationSanta MonicaUSA
  2. 2.Yale UniversityNew Haven

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