TY - JOUR

T1 - Non-autonomous Linear Quadratic Non-cooperative Differential Games with Continuous Updating

AU - Kuchkarov, Ildus

AU - Petrosian, Ovanes

AU - Li, Yin

N1 - Kuchkarov, I., Petrosian, O., & Li, Y. (2023). Non-autonomous Linear Quadratic Non-cooperative Differential Games with Continuous Updating. Contributions to Game Theory and Management, 15, 132-154. Retrieved from https://gametheory.spbu.ru/article/view/14587

PY - 2022

Y1 - 2022

N2 - The subject of this paper is a non-autonomous linear quadratic case of a differential game model with continuous updating. This class of differential games is essentially new where it is assumed that, at each time instant, players have or use information about the game structure defined on a closed time interval with a fixed duration. During the interval information about motion equations and payoff functions of players updates. It is non-autonomy that simulates this effect of updating information. A linear quadratic case for this class of games is particularly important for practical problems arising in the engineering of human-machine interaction. Here we define the Nash equilibrium as an optimality principle and present an explicit form of Nash equilibrium for the linear quadratic case. Also, the case of dynamic updating for the linear quadratic differential game is studied and uniform convergence of Nash equilibrium strategies and corresponding trajectory for a case of continuous updating and dynamic updating is demonstrated.

AB - The subject of this paper is a non-autonomous linear quadratic case of a differential game model with continuous updating. This class of differential games is essentially new where it is assumed that, at each time instant, players have or use information about the game structure defined on a closed time interval with a fixed duration. During the interval information about motion equations and payoff functions of players updates. It is non-autonomy that simulates this effect of updating information. A linear quadratic case for this class of games is particularly important for practical problems arising in the engineering of human-machine interaction. Here we define the Nash equilibrium as an optimality principle and present an explicit form of Nash equilibrium for the linear quadratic case. Also, the case of dynamic updating for the linear quadratic differential game is studied and uniform convergence of Nash equilibrium strategies and corresponding trajectory for a case of continuous updating and dynamic updating is demonstrated.

KW - Differential games with continuous updating

KW - nash equilibrium

KW - Linear quadratic differential games

KW - non-autonomous

M3 - Article

SP - 132

EP - 154

JO - Contributions to Game Theory and Management

JF - Contributions to Game Theory and Management

SN - 2310-2608

IS - 15

ER -