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Taking Turns in Continuous Time

This paper studies the impact of continuous time interactions on the dynamics of battle of the sexes games with laboratory experiments. In discrete time battle of the sexes games, players often interact with alternating strategies and switch between two pure Nash equilibria, which is difficult to coordinate in continuous time because the players must determine both the order of alternations and how long to remain at each pure equilibrium. Overall, laboratory subjects behave differently in the two time environments. Although the continuous time interactions accelerate the initial convergence to one of the pure strategy equilibria and divergence from mismatches, they undermine the subjects' subsequent ability to coordinate moves from one equilibrium to the other. Compared to the alternating pattern in discrete time, the pattern in continuous time is unstable and diverse, and the transitions are mainly motivated by the disadvantaged subjects. The difficulty in alternation also slows the learning process in continuous time.