Commitment and Time Consistency : A Game-Theoretic Discussion

The paper offers a game-theoretic framework for discussing commitment and time consistency. We show when a commitment (or just the appearance of one) is valuable, how valiable it is, and whether the commitment is time consistent. We formulate restrictions on the set of eligible commitments. These restrictions correspond to the open-loop programming format, and we call the restrictions policy formation. We give a game-theoretic depiction of Fisher's savings-taxation model of time consistency. This depiction shows in a game tree the essential lessons of the model. The emphasis is on definition, examples, and interpretation. The paper contains no formal propositions. Our goal is to show that the concepts developed are useful for understanding commitment and time consistency, for modeling situations with these characteristics, and for achieving general results