In this paper we consider binary relations which are reflexive and complete. Such binary relations are referred to in the literature as abstract games. Given an abstract game a (game)solution is a function which associates to each subset a non-empty collection of points of the subset. In this paper we provide axiomatic characterizations of the top cycle and uncovered solutions for abstract games. In a final section of the paper, the similarity between a game solution and a choice function of classical rational choice theory is exploited to axiomatically characterize the top cycle and uncovered choice functions.