Dominance solvability and cournot stability

In normal form games with single-valued best reply functions it is shown that dominance-solvability (resulting from successive elimination of dominated strategies) implies the global stability of the Cournot tatonnement process. When only two players are present, and the strategy spaces are one dimensional, these two notions actually coincide. A computational characterization of the two properties is given in a local sense as well as a sufficient condition for global dominance-solvability: an application to the Cournot-oligopoly model is proposed