This paper proposes a new interpretation of non-cooperative games that shows why the unilateralism of best-reply reasoning fails to capture the mutuality of strategic interdependence. Drawing on an intersubjective approach to theorizing individual agency in shared context, including a non-individualistic model of common belief without infinite regress, the paper develops a general model of a 2 × 2 simultaneous one-shot non-cooperative game and applies it to games including Hi-Lo, Stag Hunt, Prisoners’ Dilemma, Chicken, BoS and Matching Pennies. Results include High (...) as the rational choice in Hi-Lo, and Cooperate as a possible rational choice in the Prisoners’ Dilemma. (shrink)