Brownian Signals: Information Quality, Quantity and Timing in Repeated Games

Abstract

This paper examines different Brownian information structures over varying time intervals. We focus on the non-limit case, and on the trade-offs between information quality and quantity when making a decision whether to cooperate or defect in a prisoners’ dilemma game. In the best-case scenario, the information quality gains are strong enough so that agents can substitute information quantity with information quality. In the second best-case scenario, the information quality gains are weak and must be compensated for with additional information quantity. In this case, information quality improves but not quickly enough to dispense with the use of information quantity. For sufficiently large time intervals, information degrades and monitoring becomes mostly based on information quantity. The results depend crucially on the particular information structure and on the rate at which information quality improves or decays with respect to the discounting incentives.