Applied Set-Valued Analysis and Optimization

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DOI: 10.23952/asvao.5.2023.3.06
Volume 5, Issue 3, 1 December 2023, Pages 401-438

 

Abstract. In this paper, a finite-horizon two-person Nash equilibrium game for a linear time-dependent differential system with delays (point-wise and distributed) in the state variable and the players’ control variables is considered. The behaviour of each player is evaluated by its own quadratic functional to be minimized by this player. The feature of this game is that a weight matrix of the control in the functional of one player is singular (but, in general, non-zero). Due to this feature, the game itself is singular. Using the regularization method and the asymptotic analysis of the regularized Nash equilibrium game, an open-loop Nash equilibrium solution to the considered singular game is derived. Illustrative example is presented. Along with this example, two examples on non-uniqueness of open-loop Nash equilibrium solutions to the singular game are presented.

 

How to Cite this Article:
V.Y. Glizer, Solutions of one class of singular two-person Nash equilibrium games with state and control delays: Regularization approach, Appl. Set-Valued Anal. Optim. 5 (2023), 401-438.