On nonexistence of reconsideration-proof equilibrium with state variables

Reconsideration-proofness is a solution concept proposed by Kocherlakota (Games Econ Behav 15(1):33–54, 1996) for infinite horizon single-player problems in which time inconsistency is important. Kocherlakota’s (1996) definition has a limitation: it is not applicable to environments with state variables. The limitation is important because many time-inconsistent problems have state variables. This paper displays a natural generalization of reconsideration-proofness to environments with state variables, and shows that it leads to nonexistence in three examples. Such nonexistence contrasts with the general existence theorem obtained in environments without state variables in Kocherlakota (1996). In the first two examples, existence can be recovered with a modification in the solution concept. In the last example, nonexistence occurs even with the modified solution concept. Insights about further research are derived from these nonexistence results.