[The purpose of this paper is to reconsider the theory of Pareto optimal redistribution from a game-theoretic point of view. We define an income redistribution game in strategic form, which may allow many varieties of utilityinterdependencies. The strategy of each individual is a vector that describes a plan of transfers from him to every other individual. The results state that while a Pareto optimal redistribution is always achieved by a Nash equilibrium in the two-person case, it is not so when there are more than two individuals. The sufficient condition we derived seems unlikely to be satisfied in general.]