Abstract
The usual properties of a characteristic function game were derived byvon Neumann andMorgenstern from the properties of a game in normal form. In this paper we give a linear programming principle for the calculation of the characteristic function. The principle is a direct application ofCharnes' linear programming method for the calculation of the optimal strategies and the value of a two-person zero-sum game. The linear programming principle gives another method for proving the standard properties of a characteristic function when it is derived from a game in normal form. Using an idea originated byCharnes for two person games, we develop the concept of a constrainedn-person game as a simple, practical extension of ann-person game. However the characteristic function for a constrainedn-person game may not satisfy properties, such as superadditivity, usually associated with a characteristic function.
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References
Charnes, A.: Constrained Games and Linear Programming, Proceedings of the National Academy of Sciences,39, No. 7, 639–641, 1953.
Charnes, A., andW. W. Cooper: Management Models and Industrial Applications of Linear Programming, Vol. II, John Wiley and Sons, New York 1961.
von Neumann, J., andO. Morgenstern: Theory of Games and Economic Behavior, John Wiley and Sons, New York 1953.
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This research was partly supported by ONR Research Contracts N00014-67-A-0126-0008 and N00014-67-A-0126-0009 and by a research fellowship from Resources for the Future, Inc.
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Charnes, A., Sorensen, S. Constrainedn-person games. Int J Game Theory 3, 141–158 (1974). https://doi.org/10.1007/BF01763254
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DOI: https://doi.org/10.1007/BF01763254