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.

中文翻译：

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不确定离散时间博弈中的开环鲁棒均衡

本文解决了受某种时变不确定扰动影响的离散时间 N 玩家博弈的问题。开发了关于 i-player 的不确定性最坏情况的哲学，以推导出开环鲁棒纳什均衡存在的充分必要条件。这些条件是根据一组具有某些边界条件的离散时间 Riccati 类型方程的可解性来表示的。作为解决方案的说明，开发了一个具有不确定的季节性需求波动的两级供应链协调的模拟。