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Markov Perfect Nash Equilibrium in stochastic differential games as solution of a generalized Euler Equations System [PDF]

, 2008
This paper gives a new method to characterize Markov Perfect Nash Equilibrium in stochastic differential games by means of a set of Generalized Euler Equations.
Rincón-Zapatero, Juan Pablo, Josa-Fombellida, Ricardo +1 more
core +1 more source

Cemracs 2017: numerical probabilistic approach to MFG [PDF]

ESAIM: Proceedings and Surveys, 2019
This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type.
Angiuli Andrea +5 more
doaj +1 more source

Stochastic Differential Games in a Non-Markovian Setting [PDF]

SIAM Journal on Control and Optimization, 2005
Stochastic differential games are considered in a non-Markovian setting. Typically, in stochastic differential games the modulating process of the diffusion equation describing the state flow is taken to be Markovian. Then Nash equilibria or other types of solutions such as Pareto equilibria are constructed using Hamilton--Jacobi--Bellman (HJB ...
Erhan Bayraktar, H. Vincent Poor
openaire +5 more sources

Novel Design of Slim Mould Optimizer for the Solution of Optimal Power Flow Problems Incorporating Intermittent Sources: A Case Study of Algerian Electricity Grid

IEEE Access, 2022
Nowadays, electrical power grids are facing increased penetration of renewable energy sources (RES), which result in increasing level of randomness and uncertainties for its operational quality.
Souhil Mouassa +3 more
doaj +1 more source

Asymptotic behaviours of stochastic differential delay equations [PDF]

, 2005
Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper.
Shen, Yi, Mao, Xuerong, Xuerong Mao, Yi Shen +3 more
core +4 more sources

Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models

Mathematics, 2020
We consider the indefinite, linear-quadratic, mean-field-type stochastic zero-sum differential game for jump-diffusion models (I-LQ-MF-SZSDG-JD).
Jun Moon, Wonhee Kim
doaj +1 more source

Backward-forward linear-quadratic mean-field Stackelberg games

Advances in Difference Equations, 2021
This paper studies a controlled backward-forward linear-quadratic-Gaussian (LQG) large population system in Stackelberg games. The leader agent is of backward state and follower agents are of forward state.
Kehan Si, Zhen Wu
doaj +1 more source

Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application

Advances in Difference Equations, 2017
This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information.
Yi Zhuang
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A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games

Aerospace
This paper investigates three-dimensional pursuit problems in noncooperative stochastic differential games. By introducing a novel polynomial value function capable of addressing high-dimensional dynamic systems, the forward–backward stochastic ...
Yu Bai, Di Zhou, Zhen He
doaj +1 more source

Stochastic Differential Games

Journal of Differential Equations, 1972
Consider a stochastic differential system of \(m\) equations \[ d\xi(t)=f(t,\xi(t), y_1,\ldots, y_N)\,dt+ \sigma(t, \xi(t))\,dw(t),\quad \xi(s) =x_0, \] where the player \(y_i\) chooses a control function with values in a control set \(Y_i\). Denote by \(\tau\) the exit time of \(\xi(t)\) from a cylinder \(\{s
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stochastic differential game