On the uniqueness of the Nash solution in Linear-Quadratic differential Games

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Abstract

This paper contains an investigation of existence, uniqueness, admissibility and reliability of Nash equilibrium solutions in 2-person Linear-Quadratic Nonzero-Sum Differential Games (LQNZSDG) and for different information structures for either player. Depending on the information structures of both players, either uniqueness is established or nonuniqueness and inadmissibility of the Nash solution is exhibited. It constitutes the first report on these (information structure)-dependent uniqueness properties of Nash solutions. In order to resolve the dilemma for the case of nonunique solutions, random perturbations are included in the state dynamics and existence of unique insensitive equilibrium solution is established for the resulting LQNZSDG.

Original languageEnglish (US)
Pages (from-to)65-90
Number of pages26
JournalInternational Journal of Game Theory
Volume5
Issue number2-3
DOIs
StatePublished - Jun 1 1976
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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