Time Consistency in Cooperative Differential Games: A Tutorial

How can a cooperative agreement made at the start of a dynamic game can be sustained over time? Early work has avoided this question by supposing that the players sign binding agreements. This assumption is hard to accept from a theoretical perspective, and a practical one as well. Conceptually, there is no reason to believe that rational players would stick to an agreement if they can achieve a better outcome by abandoning, no matter what they have announced before. At an empirical level, it suffices to look at the number of disputes (between spouses, business partners, countries, etc.) in the courts to convince ourselves that binding agreements are not so binding. Scholars in dynamic games have followed different lines of thoughts to answer the question. This tutorial reviews one of them, namely time consistency, a concept which has also been termed dynamic individual rationality, sustainability, dynamic stability, agreeability, or acceptability.