Time-Inconsistent Stochastic Linear-quadratic Differential Game
Qinglong Zhou, Gaofeng Zong

TL;DR
This paper studies a complex stochastic differential game with time-inconsistent objectives, proposing a new equilibrium concept, deriving conditions for equilibrium strategies, and providing explicit solutions in special cases.
Contribution
It introduces a novel equilibrium strategy for time-inconsistent stochastic linear-quadratic differential games and derives explicit solutions in deterministic, one-dimensional cases.
Findings
Established a sufficient condition for equilibrium strategies.
Derived explicit equilibrium strategies in one-dimensional deterministic cases.
Proved uniqueness of the equilibrium strategy in these cases.
Abstract
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and derived a sufficient conditions for equilibrium strategies via a system of forward-backward stochastic differential equations. When the state is one-dimensional and the coefficients are all deterministic, we find an explicit equilibrium strategy. The uniqueness of such equilibrium strategy is also given.
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Taxonomy
TopicsEconomic theories and models · Stochastic processes and financial applications · Climate Change Policy and Economics
