Dutta's minimal covering set and Shapley's saddles

We prove the existence and uniqueness of the weak saddle, a solution due to Shapley, for a class of zero-sum games including tournament games, as defined by Laffond, Laslier, and Le Breton. We then show that the minimal covering set of a tournament, proposed by Dutta, coincides with the weak saddle of the corresponding tournament game. This provides a positive foundation for the minimal covering set and yields, as corollaries, Dutta's existence and uniqueness theorems for the minimal covering set. Journal of Economic Literature Classification Numbers: C70, C72. (C) 1996 Academic Press, Inc.