The role of information in repeated games with frequent actions

We show that the ways incentives can be provided during dynamic interaction depend very crucially on the manner in which players learn information. This conclusion is established in a general stationary environment with noisy public monitoring and frequent actions. The monitoring process can be represented by a sum of a multi-dimensional Brownian component and a jump process. We show that jumps can be used to provide incentives both with transfers and value burning while continuous information can be used to provide incentives only with transfers. Also, it is asymptotically optimal to use the cumulative realization of the Brownian component linearly. Additionally, we approximate the equilibrium payoff set for fixed small discount rates as the periods become short by a series of linear programming problems. These problems highlight how the two types of information can be used to provide incentives.