A note on the welfare of a sophisticated time-inconsistent decision-maker - Sebastian Kodritsch (Wissenschaftszentrum Berlin für Sozialforschung (WZB), 2015)
I examine the circumstances under which a sophisticated time-inconsistent decisionmaker (i) will not or (ii) need not severely miscoordinate her behavior across time, in the sense of following a course of action which fails to be Pareto-optimal for the sequence of temporal selves of the individual (Laibson [1994] and O'Donoghue and Rabin [1999] provide prominent instances of such miscoordination). Studying the standard solution concept for this case - Strotz-Pollak equilibrium - in general decision problems with perfect information, I establish two results: first, for finite-horizon problems without indifference, essential consistency (Hammond [1976]) is sufficient for choice to be Pareto-optimal. Second, if the decision problem satisfies a certain history-independence property, whenever an equilibrium outcome fails to be Pareto-optimal, it is Pareto-dominated by another equilibrium outcome, leading to an existence result for a Pareto-optimal solution.
Keywords: C72; D11; D60; D74; D90; 330; time-inconsistency; multi-selves approach; Strotz-Pollak equilibrium; welfare; Pareto-optimality