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This paper considers a discrete-time non-cooperative M-players linear affine quadratic game of pre-specified fixed duration, affected by stochastic noise and deterministic disturbances. The last one is seen as a pernicious fictitious player looking to maximise the expected cost functions of each player. Inspired in the discrete-time robust dynamic programming, sufficient conditions for the existence of a type of robust feedback NE are given in the solution of a set of discrete-time difference equations. A formal induction proof is provided for the closed form of the obtained robust set of strategies. Two illustrative simulation examples are included, one related to the problem of coordination of a two-echelon supply chain with uncertain seasonal demand. The goal of the agents is to reduce the expected cost of storage while satisfying a partially known demand. The second example is related to a game of government debt stabilisation. Comparing the simulation with the standard Nash strategy, the robust one achieves a better performance.
Jiménez‐Lizárraga et al. (Fri,) studied this question.