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Open Loop Robust Equilibria in Uncertain Discrete Time Games

Fernando Guerrero Vélez, Manuel Jiménez Lizárraga*, and Celeste Rodriguez Carreon
International Journal of Control, Automation, and Systems, vol. 19, no. 2, pp.587-595, 2021

Abstract : This paper tackles the problem of a discrete time N players game affected by some sort of time-varying uncertain perturbation. The philosophy of the uncertainty worst case scenario with respect to the i-player is developed to derive necessary and sufficient conditions for the existence of an Open Loop Robust Nash Equilibria. Such conditions are presented in terms of the solvability of a set of discrete time Riccati type equations with some boundary conditions. As an illustration of the solution, a simulation of the coordination of a two-echelon supply chain with uncertain seasonal fluctuations in the demand is developed.

Keyword : Discrete time game, robust Nash equilibria, two echelon supply chains.

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