In a continuous-time setting, the existing notion of equilibrium strategies for time-inconsistent problems in the literature,referred to as weak equilibria, is not fully aligned with the standard definition of equilibria in the game theory in that the agentmay be willing to deviate from a given weak equilibrium strategy. To address this issue, we propose two new notions of equilibriumstrategies for time-inconsistent problems, named regular equilibria and strong equilibria. For a large class of time-inconsistentproblems, we derive sufficient conditions as well as necessary conditions for a strategy to be a regular equilibrium and to be a strong equilibrium. We examine three time-inconsistent portfolio selection problems in the literature and show that the weak equilibrium strategies derived therein are also regular equilibria but are not strong equilibria. We further provide an example to show that a weak equilibrium strategy may not be a regular equilibrium. This is a joint work with Zhaoli Jiang.

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