Inefficient Lock-in with Sophisticated and Myopic Players

Path-dependence in coordination games may lead to lock-in on inefficient outcomes, such as adoption of inferior technologies (Arthur, 1989) or inefficient economic institutions (North, 1990). We aim to find conditions under which lock-in is overcome by developing a solution concept that makes ex-ante predictions about the adaptation process following lock-in. We assume that some players are myopic, forming beliefs according to fictitious play, while others are sophisticated, anticipating the learning process of the myopic players. We propose a solution concept based on a Nash equilibrium of the strategies chosen by sophisticated players. Our model predicts that no players would switch from the efficient to the inefficient action, but deviations in the other direction are possible. Three types of equilibria may exist: in the first type lock-in is sustained, while in the other two types lock-in is overcome. We determine the existence conditions for each of these equilibria and show that the equilibria in which lock-in is overcome are more likely and the transition is faster when sophisticated players have a longer planning horizon, or when the history of inefficient coordination is shorter.