Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation

Abstract

Time inconsistency is prevalent in dynamic choice problems: a plan of actions to be taken in the future that is optimal for an agent today may not be optimal for the same agent in the future. If the agent is aware of this intrapersonal conflict but unable to commit herself in the future to following the optimal plan today, the rational strategy for her today is to reconcile with her future selves, namely to correctly anticipate her actions in the future and then act today accordingly. Such a strategy is named intrapersonal equilibrium and has been studied since as early as in the 1950s. A rigorous treatment in continuous-time settings, however, had not been available until a decade ago. Since then, the study on intra-personal equilibrium for time-inconsistent problems in continuous time has grown rapidly. In this chapter, we review the classical results and some recent development in this literature.

Quasilinearization Methods for Nonlocal Fully-Nonlinear Parabolic Systems

“…Some well-known examples are the hyperbolic discounting [11,4] and prospect theory [8] in behavioural economics. For the time-inconsistent (TIC) stochastic control problems, rigorous mathematical treatment was only available about one decade ago; see [6] for a succinct account of the latest progress. The prevailing approach, initiated in [18] and developed in [2,1], finds the subgame perfect equilibrium of the TIC dynamic choice problems.…”