The Dynamic Cognitive Hierarchy Model : A Theory of Equilibrium Switching

This paper proposes a model of equilibrium switching in coordination games such as collective participation in social changes. In our model, players are forward-looking but use level-k reasoning about their peers' choices. We find that equilibrium switching is deterministic and gradual, with higher k players switching first. In some cases, the final equilibrium is reached only after severalother equilibria are visited, where each step is Pareto improving. We completely characterize the switching paths for all coordination games with finite strict Nash equilibria, and a large class of level-k populations. The model provides a unified explanation for puzzling equilibrium switching results reported in recent experimental studies, including the direction of transition, asynchronous participation, and alternations between strict Nash equilibria