Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time

Yu-Jui Huang () and Zhou Zhou ()
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Yu-Jui Huang: Department of Applied Mathematics, University of Colorado, Boulder, Boulder, Colorado 80309
Zhou Zhou: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia

Mathematics of Operations Research, 2021, vol. 46, issue 2, 428-451

Abstract: A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined and allows for unambiguous economic interpretation. The terms “strong equilibria” and “weak equilibria” are coined for controls under the new and standard definitions, respectively. When the state process is a time-homogeneous continuous-time Markov chain, a careful asymptotic analysis gives complete characterizations of weak and strong equilibria. Thanks to the Kakutani–Fan fixed-point theorem, the general existence of weak and strong equilibria is also established under an additional compactness assumption. Our theoretic results are applied to a two-state model under nonexponential discounting. In particular, we demonstrate explicitly that there can be incentive to deviate from a weak equilibrium, which justifies the need for strong equilibria. Our analysis also provides new results for the existence and characterization of discrete-time equilibria under infinite horizon.

Keywords: Primary: 60J27; secondary: 91A13; Primary: games/group decisions: noncooperative; secondary: Dynamic programming/optimal control: Markov finite state; time-inconsistency; stochastic control; continuous-time Markov chain; strong equilibria; weak equilibria; nonexponential discounting (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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