Vol. 34, No. 2, 1970

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The four-person constant-sum games; Discriminatory solutions on the main diagonal

Guillermo Owen

Vol. 34 (1970), No. 2, 461–480

It is known that every four-person constant-sum game has discriminatory solutions. In this paper, we consider the games on the “main diagonal” which are symmetric in the first three players, and look for solutions which discriminate the fourth player, i.e., give him a constant amount. The seven types of solutions are catalogued, and necessary and sufficient conditions are found for the solution of the 3-person game to expand to a solution of the 4-person game. Finally, this paper determines the amounts which the fourth, discriminated player is allowed to receive in order that a solution of each of the seven types exist.

Mathematical Subject Classification
Primary: 90.70
Received: 5 July 1967
Revised: 1 December 1969
Published: 1 August 1970
Guillermo Owen