Philosophers using game-theoretical models of human interactions have, I argue, often overestimated what sheer rationality can achieve. (References are made to David Gauthier, David Lewis, and others.) In particular I argue that in coordination problems rational agents will not necessarily reach a unique outcome that is most preferred by all, nor a unique 'coordination equilibrium' (Lewis), nor a unique Nash equilibrium. Nor are things helped by the addition of a successful precedent, or by common knowledge of generally accepted personal principles. (...) Commitments like those generated by agreements may be necessary for rational expectations to arise. Social conventions, construed as group principles (following the analysis in my book On Social Facts), would suffice for this task. (shrink)