Mappings conjugate to multivalued mappings of topological spaces, and their application to dynamical games

Associated with multivalued mappings of a topological space $X$ into a topological space $Y$ are conjugate mappings of the set of upper (lower) semicontinuous real functions on $Y$ into the set of real functions on $X$. It is shown that to compactvalued upper semicontinuous mappings of $X$ into $Y$ there correspond mappings of the set of upper (lower) semicontinuous real functions on $Y$ into the set of upper (lower) semicontinuous real functions on $X$.
The properties of the conjugate mappings are studied, and their applications to dynamical games are considered.
Bibliography: 7 titles.