Int. Journal of Game Theory, Vol. 9, Issue 4, page 233- 245. QPhysica- Verlag, Vienna. Some Results on Zero-Sum Games with Incomplete Information: The Dependent Case By J.P. Ponssard, Paris 1 ). and S. Sorin, Paris 2) Abstract: In games with incomplete information, the players' states of information may be deter- mined either through independent chance moves or through a unique one. Generally, a unique chance move generates some dependance in the players' state of information thus giving rise to significant complications in the analysis. However, it turns out that many results obtained in the simpler independent case have their counterpart in the dependent one. This is proved in this paper for several previous results of the authors. 1. Introduction The class of games under consideration is the following. (i) Let G be a finite two person game tree with its rules (sequence of moves and infor- mation sets). (ii) Let M h be the zero sum payoff associated with a play h of G, M h is a discrete ran- dom variable defined by: Prob (M h = mkh) = pk where p CP (the simplex of R K) is a common knowledge probability. Moreover the private information structure is the following [Mertens/ Zamir ]. There are two partitions ofK = {1 .... , k ..... L) denoted by: KI: KI1, = ;KI, l ..... such that if chance chooses k according to p, player 1 - the maximizer - is informed of a and player 2 - the minimizer - is informed of b where k belongs to K2 N K 11. 1) j.p. Ponssard, Centre de Recherche en Gestion, Ecole Polytechnique, 17 rue Descartes F-75005 Paris, France. 2) S. Sorin, Laboratoire d'Econom~trie, Universit~ Paris VI, 4 Place Jussieu F-75230 Paris Cedex 05, France.