Time Consistency and Related Concepts

We give rigorous game-theoretic meaning to the Stackelberg notions of time inconsistency and to the idea of commitment being of value (or sequential irrationality). Time inconsistency treats desirable deviations only along the path, whereas sequential irrationality treats deviations everywhere in the tree. We establish four relationships: time inconsistency implies sequential irrationality; sequential irrationality implies and is implied by the failure of subgame perfect equilibrium; and time consistency implies Nash equilibrium. (In the last case the restrictions are numerous.) We show also that no other relationships are valid. Our basic results are easily gleaned from the schema provided in Figure 1 (which follows typescript page 29)