Current debates in social ontology are dominated by approaches that view institutions either as rules or as equilibria of strategic games. We argue that these two approaches can be unified within an encompassing theory based on the notion of correlated equilibrium. We show that in a correlated equilibrium each player follows a regulative rule of the form ‘if X then do Y’. We then criticise Searle’s claim that constitutive rules of the form ‘X counts as Y in C’ are fundamental building blocks for institutions, showing that such rules can be derived from regulative rules by introducing new institutional terms. Institutional terms are introduced for economy of thought, but are not necessary for the creation of social reality.