On the Notions of Equilibria for Time-Inconsistent Stopping Problems in Continuous Time

Bayraktar, Erhan; Zhang, Jingjie; Zhou, Zhou

doi:10.2139/ssrn.3448620

Cited by 6 publications

(4 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Throughout this paper, we focus on relaxed type policies, represented as P(U )-valued controls, rather than U -valued controls, since the family of U -valued controls is generally insufficient for addressing time-inconsistent optimization problems. Indeed, [8] shows that a U -valued equilibrium may not even exist for a time-inconsistent stochastic control problem unless certain strict concavity structures are assumed. Therefore, a U -valued equilibrium may also not exist for the MFG in the context of time-inconsistency, and it is natural to consider the larger family of P(U )-valued policies, which contains all U -valued policies by treating a control value u as a Dirac measure in P(U ).…”

Section: Mean Field Games With Time-inconsistencymentioning

confidence: 99%

“…As proposed in Strotz [27], a sophisticated agent treats a time-inconsistent control problem as an intertemporal game among current self and future selves and looks for a subgame perfect Nash equilibrium: a consistent strategy that, given the future selves follow this strategy, the current self has no incentive to deviate from it. Nash equilibrium in time-inconsistent stochastic controls has been widely explored; for recent developments, see [30,16,21,9,8,7] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite State Mean Field Games with Wright–Fisher Common Noise as Limits ofN-Player Weighted Games

et al. 2022

View full text Add to dashboard Cite

Forcing finite state mean field games by a relevant form of common noise is a subtle issue, which has been addressed only recently. Among others, one possible way is to subject the simplex valued dynamics of an equilibrium by a so-called Wright–Fisher noise, very much in the spirit of stochastic models in population genetics. A key feature is that such a random forcing preserves the structure of the simplex, which is nothing but, in this setting, the probability space over the state space of the game. The purpose of this article is, hence, to elucidate the finite-player version and, accordingly, prove that N-player equilibria indeed converge toward the solution of such a kind of Wright–Fisher mean field game. Whereas part of the analysis is made easier by the fact that the corresponding master equation has already been proved to be uniquely solvable under the presence of the common noise, it becomes however more subtle than in the standard setting because the mean field interaction between the players now occurs through a weighted empirical measure. In other words, each player carries its own weight, which, hence, may differ from [Formula: see text] and which, most of all, evolves with the common noise.

show abstract

Section: Mean Field Games With Time-inconsistencymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite State Mean Field Games with Wright–Fisher Common Noise as Limits ofN-Player Weighted Games

et al. 2022

View full text Add to dashboard Cite

show abstract

“…for y ∈ X h , and we write E h to emphasis that the expectation is under the binomial-tree setting. Following [4], we define (ε-)equilibria in the binomial-tree model as follows.…”

Section: Time and State Space Discretizationmentioning

confidence: 99%

Short Communication: Stability of Time-Inconsistent Stopping for One-Dimensional Diffusions

Bayraktar

Wang

Zhou

2022

SIAM J. Finan. Math.

View full text Add to dashboard Cite

For time-inconsistent stopping in a one-dimensional diffusion setup, we investigate how to use discrete-time models to approximate the original problem. In particular, we consider the value function V (•) induced by all mild equilibria in the continuous-time problem, as well as the value V h (•) associated with the equilibria in a binomial-tree setting with time step size h. We show that lim h→0+ V h ≤ V . We provide an example showing that the exact convergence may fail. Then we relax the set of equilibria and consider the value V h ε (•) induced by ε-equilibria in the binomial-tree model. We prove that lim ε→0+ lim h→0+ V h ε = V .

show abstract

“…The notion of optimal equilibria have recently been generalized in Bayraktar, Zhang, and Zhou [2], to reflect the subtle differences of how an equilibrium is formulated in Huang and Zhou [18], [14], and [6]. Also, the existence of optimal equilibria for a time-inconsistent dividend problem has been analyzed in detail by Jin and Zhou [20].…”

Section: Introductionmentioning

confidence: 99%

Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems

Huang,

Wang

2020

Preprint

View full text Add to dashboard Cite

We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience in behavioral economics. On strength of probabilistic potential theory, we establish the existence of an optimal equilibrium among a sufficiently large collection of equilibria, consisting of finely closed equilibria satisfying a boundary condition. This generalizes the existence of optimal equilibria for one-dimensional stopping problems in prior literature.

show abstract

On the Notions of Equilibria for Time-Inconsistent Stopping Problems in Continuous Time

Cited by 6 publications

References 23 publications

Finite State Mean Field Games with Wright–Fisher Common Noise as Limits ofN-Player Weighted Games

Finite State Mean Field Games with Wright–Fisher Common Noise as Limits ofN-Player Weighted Games

Short Communication: Stability of Time-Inconsistent Stopping for One-Dimensional Diffusions

Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems

Contact Info

Product

Resources

About