scholarly journals Continuous-time zero-sum stochastic game with stopping and control

2020 ◽  
Vol 48 (6) ◽  
pp. 715-719
Author(s):  
Chandan Pal ◽  
Subhamay Saha
Keyword(s):  
Continuous Time ◽  
Stochastic Game ◽  
Time Zero ◽  
Zero Sum ◽  
And Control

scholarly journals Approximation of value function of differential game with minimal cost

2021 ◽  
Vol 31 (4) ◽  
pp. 536-561
Author(s):  
Yu.V. Averboukh
Keyword(s):  
Differential Game ◽  
Continuous Time ◽  
Bellman Equation ◽  
Value Function ◽  
Stochastic Game ◽  
Inequality Constraints ◽  
Minimal Cost ◽  
Parabolic Pde ◽  
Zero Sum ◽  
The Value Function

The paper is concerned with the approximation of the value function of the zero-sum differential game with the minimal cost, i.e., the differential game with the payoff functional determined by the minimization of some quantity along the trajectory by the solutions of continuous-time stochastic games with the stopping governed by one player. Notice that the value function of the auxiliary continuous-time stochastic game is described by the Isaacs–Bellman equation with additional inequality constraints. The Isaacs–Bellman equation is a parabolic PDE for the case of stochastic differential game and it takes a form of system of ODEs for the case of continuous-time Markov game. The approximation developed in the paper is based on the concept of the stochastic guide first proposed by Krasovskii and Kotelnikova.

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