How do institutions evolve when subject to random shocks and uncertainty? And how does this affect the convergence of informal and formal institutions? We propose to model these changes in an evolutionary game in which we distinguish between the Meta set of all existing and potential institutional arrangements and the de facto set of institutions that agents actually choose to uphold in equilibrium. In general, we formulate new stochastic evolutionary dynamics with drift and time-varying mutation rates, thereby relaxing some of the more rigid features of evolutionary games which limit their adaptability to social phenomena. Specifically, this provides a plausible model of institutional change in which, at the Meta level, the destruction of old institutions and the creation of new are unpredictable, which in turn defines, at the de facto level, the extent of agents’ bounded rationality and choice of strategy. We distinguish between the medium run – when the risk dominant, more “rational choice” strategy persists – vs. the long and ultra-long run when complex change may cause too much drift away from the risk dominant strategy in equilibrium. This provides a richer, and more intuitive framework in which to consider the scope of path dependence and the role of randomness in the endogenous evolution of social institutions.