Abstract
In this paper, we introduce and study alpha-irresolute multifunctions, and some of their properties are studied. The properties of alpha-compactness and alpha-normality under upper alpha-irresolute multifunctions are topological properties. Also, we prove that the composition of two upper and lower alpha-irresolute multifunctions is alpha-irresolute. We apply the results of alpha-irresolute multifunctions to topological games. Upper and lower topological games are introduced. The set of places for player ONE in upper topological games may guarantee a gain is semi-closed. Finally, some optimal strategies for topological games are defined and studied.