Coordination, learning, and delay

This paper studies how the introduction of social learning with costs to delay affects coordination games with incomplete information. We present a tractable noisy dynamic coordination game with social learning and costs to delay. We show that this game has a unique monotone equilibrium. A comparison of the equilibrium of the dynamic game with the equilibria of analogous static coordination games explicates the role of social learning. The analysis is carried out for both endogenous and exogenous order of moves in the dynamic game. In the limit as noise vanishes, social welfare is strictly ranked in these games, with the highest welfare achieved in the dynamic game with endogenous ordering. We demonstrate that exogenous asynchronicity is not a substitute for endogenous asynchronicity. We also show that under endogenous ordering, as noise vanishes, the efficiency of coordination is maximized at intermediate costs to delay. The robustness of these results is illustrated numerically away from the complete information limit, when closed forms are not available. Our results have implications for the initial public offerings of debt, as well as for the adoption of new technology under incomplete information.