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Robust open-loop Nash equilibria in the noncooperative LQ game revisited

Engwerda,Jacob
Abstract
This paper reconsiders existence of worst-case Nash equilibria in noncooperative multi-player differential games, this, within an open-loop information structure. We show that these equilibria can be obtained by determining the open-loop Nash equilibria of an associated differential game with an additional initial state constraint. For the special case of linear-quadratic differential games, we derive both necessary and sufficient conditions for solvability of the finite planning horizon problem. In particular, we demonstrate that, unlike in the standard linear-quadratic differential game setting, uniqueness of equilibria may fail to hold. A both necessary and sufficient condition under which there is a unique equilibrium is provided. A sufficient existence condition for a unique equilibrium is derived in terms of a Riccati differential equation. Consequences for control policies are demonstrated in a simple debt stabilization game.
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2017-09
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Tilburg University Research Output Collection
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robust control, noncooperative differential games, linear optimal control, Riccati equations
Citation
Engwerda, J 2017, 'Robust open-loop Nash equilibria in the noncooperative LQ game revisited', Optimal Control Applications & Methods, vol. 38, no. 5, pp. 795-813. https://doi.org/10.1002/oca.2290
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https://hdl.handle.net/20.500.14602/66111
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