By using the uniform continuity of two onto maps, this paper further explores stronger forms of Kato’s chaos, sensitivity, and accessibility of Cournot maps. In particular, the sensitivity, the collective sensitivity, the accessibility, and the collective accessibility of the compositions of two reaction functions are studied. It is observed that a Cournot onto map H on a product space is sensitive (collectively sensitive, collectively accessible, accessible, or collectively Kato chaotic) if and only if the restriction of the map H2 to the MPE-set is sensitive as well. Several examples are given to show the necessity of the reaction functions being continuous onto maps.
