Threats to the stability of liberal democracies are of obvious contemporary import. Concern with stability runs through John Rawls’s work. The stability that concerned him was that of fundamental terms of cooperation. Rawls long believed that the terms which would be stable were his two principles, but he eventually conceded that even a well-ordered society was more likely to be characterized by “justice pluralism” than by consensus on his own conception of justice. Contemporary liberal democracies, too, are divided about what (...) justice demands. I believe Rawls’s treatment of stability can help us understand the conditions under which fundamental terms of cooperation can be stable under non-ideal conditions such as ours. But because Rawls never worked through the consequences of his concession, his view needs to be developed before we can draw on it. Rawls’s treatment makes use of elementary game theory. Thus in _Theory of Justice_ he said -- and in _Political Liberalism_ he implied -- that stability would result from citizens with a sense of justice “playing” strategies which combined for what was, in effect, a Nash equilibrium. I argue that his concession requires a new conception of stability and implies that Rawls cannot appeal to a Nash equilibrium to show how stability would be maintained. His concession therefore forces open a troubling gap in his analysis. I fill that gap by proposing a weaker equilibrium concept that serves Rawlsian purposes. I conclude with what this project suggests for challenges facing the fragile liberal democracies of our own time. (shrink)