Linear-Quadratic Stochastic Differential Games with General Noise Processes

Duncan, Tyrone E.

doi:10.1007/978-3-319-00669-7_2

Cited by 22 publications

(4 citation statements)

References 14 publications

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“…Subsequently, Sun [20] furthered the study of Problem (DG) T , revealing fundamental properties of this class of games and illustrating differences between stochastic and deterministic cases. Bardi-Priuli [1] delved into ergodic nonzero-sum LQ stochastic differential games with N players, while Duncan [7] investigated a class of zero-sum LQ stochastic differential games with the noise process being an arbitrary square-integrable stochastic process with continuous sample paths. Sun-Yong-Zhang [27] tackled the infinite horizon version of Problem (DG) T , followed by additional work of Li-Shi-Yong [11] incorporating mean-field terms.…”

Section: Introductionmentioning

confidence: 99%

Reinforcement learning for exploratory linear-quadratic two-person zero-sum stochastic differential games

Sun

Jia

2023

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Reinforcement learning for exploratory linear-quadratic two-person zero-sum stochastic differential games

Sun

Jia

2023

Applied Mathematics and Computation

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“…Different methods to solve MFTG have been extensively studied. Some of these methods are Stochastic Maximum Principle [5]- [7], Dynamic Programming Principle [8], Wiener Chaos Expansion [9], and the Direct Method [10]- [15]. Depending on the selected methodology to solve the aforementioned game-theoretical problem, one might obtain a solution expressed in terms of either Ordinary or Partial Differential Equations.…”

Section: Introductionmentioning

confidence: 99%

A MatLab-Based Mean-Field-Type Games Toolbox: Continuous-Time Version

Barreiro-Gómez

Tembiné

2019

IEEE Access

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In this paper, we present a user-friendly MatLab-based Mean-Field-Type Games (MFTG) Toolbox that allows simulating a diversity of scalar-valued and matrix-valued MFTG problems for an arbitrary number of players, e.g., non-cooperative, fully-cooperative and co-opetitive approaches. We present details of each one of the developed tools together with the corresponding pseudo codes, and several illustrative examples. In addition, we provide the 20 functions composing the MFTG toolbox to freely download.INDEX TERMS Mean-field-type games, simulations, MatLab-based toolbox.

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“…For LQG control and LQG zero-sum games, it can be shown that a simple square completion method provides an explicit solution to the problem. It was successfully developed and applied by Duncan et al [6][7][8][9][10][11] in the mean-field-free case. Interestingly, the method can be used beyond the class of LQG framework.…”

Section: Introductionmentioning

confidence: 99%

“…To some extent, most of the risk-neutral versions of these optimal controls are analytically and numerically solvable [6,7,9,11,24]. On the other hand, the linear quadratic robust setting naturally appears if the decision makers' objective is to minimize the effect of a small perturbation and related variance of the optimally controlled nonlinear process.…”

Section: Introductionmentioning

confidence: 99%

Linear–Quadratic Mean-Field-Type Games: A Direct Method

Duncan

Tembiné²

2018

Games

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Abstract:In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman-Kolmogorov equations or backward-forward stochastic differential equations of Pontryagin's type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear-quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.

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Linear-Quadratic Stochastic Differential Games with General Noise Processes

Cited by 22 publications

References 14 publications

Reinforcement learning for exploratory linear-quadratic two-person zero-sum stochastic differential games

Reinforcement learning for exploratory linear-quadratic two-person zero-sum stochastic differential games

A MatLab-Based Mean-Field-Type Games Toolbox: Continuous-Time Version

Linear–Quadratic Mean-Field-Type Games: A Direct Method

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