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.
