Call It a Day: History Dependent Stopping Behavior

In this paper, we provide evidence of history-dependent stopping behavior. Using data from an online chess platform, we estimate a dynamic discrete choice model in which an agent may have time non-separable preferences over the stochastic outcomes of their actions. We show that the agent's decisions cannot be reconciled in a model with time separable preferences and that there is substantial heterogeneity in preferences across players. In particular, there are two types of people: those who get discouraged by a loss and stop, and others, who get encouraged by failure and keep playing until a win. We show how to leverage the information about an agent's type in market design to achieve various welfare goals. A counterfactual analysis demonstrates that a matching algorithm that incorporates stopping behavior can significantly increase the length of play.