Endogenous timing of actions under conflict between two types of second mover advantage

In this model, two players, who are heterogeneous in information quality, compete with each other with perfect information about the other player's information quality. The less-informed player has an incentive to delay her action in order to gain more information. The more-informed player also intends to delay her action, not through a desire to learn but rather to prevent the less-informed player from gaining information. Hence, if a waiting option is available, both players want to delay their actions and the conflict between the two types of second mover advantage yields a delay race. Although both players can benefit from a delay, the gain from a delay in order to learn is greater than that from a delay intended to prevent the other from learning. Therefore, the cost for a delay plays an important role in characterizing the equilibrium, and if the sequential timing of actions is derived in a pure equilibrium, the leader will be the more-informed player. If a given cost for a delay is sufficiently low, the only equilibrium is a mixed equilibrium. Interestingly, in that equilibrium, the existence of the first-mover advantage from being imitated is also derived.