Robust open-loop Nash equilibria in the non-cooperative LQ game revisited

J.C. Engwerda

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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.
Original languageEnglish
Title of host publicationProceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014)
Place of PublicationGroningen
PublisherUniversity of Groningen
Pages200-207
ISBN (Print)9789036763219
DOIs
Publication statusPublished - Jul 2014
Event21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014) - University of Groningen, Groningen, Netherlands
Duration: 7 Jul 201411 Jul 2014

Conference

Conference21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014)
CountryNetherlands
CityGroningen
Period7/07/1411/07/14

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Keywords

  • robust control
  • noncooperative differential games
  • linear optimal control
  • Riccati equations

Cite this

Engwerda, J. C. (2014). Robust open-loop Nash equilibria in the non-cooperative LQ game revisited. In Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014) (pp. 200-207). Groningen: University of Groningen. https://doi.org/10.1002/oca.2290