A time-inconsistent Dynkin game: from intra-personal to inter-personal equilibria

Huang, Yu‐Jui; Zhou, Zhou

doi:10.1007/s00780-021-00468-1

Cited by 8 publications

(1 citation statement)

References 41 publications

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“…The development for theory of time-inconsistent stopping is more recent, and we refer to [12,10,11,13,15,6,5,3,19,2,1,14]. Let us also mention the work [17] which analyzes a time-inconsistent Dynkin game, and [18] which considers a time-inconsistent controller-stopper problem. It is worth to mention that most of the papers on time-inconsistent control and stopping focus on the characterization of equilibria.…”

Section: Introductionmentioning

confidence: 99%

Stability of Equilibria in Time-inconsistent Stopping Problems

Bayraktar¹,

Wang²,

Zhou³

2022

Preprint

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We investigate the stability of equilibrium-induced optimal values with respect to (w.r.t.) reward functions f and transition kernels Q for time-inconsistent stopping problems under nonexponential discounting in discrete time. First, with locally uniform convergence of f and Q equipped with total variation distance, we show that the optimal value is semi-continuous w.r.t. (f, Q). We provide examples showing that continuity may fail in general, and the convergence for Q in total variation cannot be replaced by weak convergence. Next we show that with the uniform convergence of f and Q, the optimal value is continuous w.r.t. (f, Q) when we consider a relaxed limit over ε-equilibria. We also provide an example showing that for such continuity the uniform convergence of (f, Q) cannot be replaced by locally uniform convergence.

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