Hyperbolic Discounting with Random Gratification

Facundo Piguillem and Liyan Shi

No 20579, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: We analyze the dynamic problem of decision makers with quasi-hyperbolic discounting and random shocks to temptation. We show that this problem is equivalent to that of a standard consumer-saver who assigns biased weights to future shocks. This equivalence provides a straightforward methodology for finding, theoretically and numerically, the Markov equilibrium with hyperbolic agents. Through this equivalent problem, we provide conditions for the existence and uniqueness of the equilibrium. If the weights constitute a probability measure, the decision maker can be interpreted as optimistically biased, ensuring a unique equilibrium with continuous decision rules and implying no value for commitment devices. Otherwise, there is intertemporal "conflict" between present and future selves: if the conflict is limited, uniqueness is guaranteed.

Keywords: Quasi-hyperbolic discounting; Optimism; Political economy; Time inconsistency (search for similar items in EconPapers)
JEL-codes: E2 E7 H1 (search for similar items in EconPapers)
Date: 2025-08
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