An axiomatization of plays in repeated games

Suppose that, in repeated games, players eventually engage in a pattern of action profiles, which we call a convention. Do some conventions seem more plausible than others? We answer axiomatically based on the principles of stability and efficient simplicity. The main solution says that conventions should be constant repetitions of a static Nash equilibrium, or such that players switch between two Pareto unranked profiles (across which they each change action). In some repeated games, this reduces the multiplicity of outcomes and even leads to uniqueness. The paper also reports experimental evidence that supports our findings.