Iterative computation of noncooperative equilibria in nonzero-sum differential games with weakly coupled players

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We study the Nash equilibria of a class of two-person nonlinear, deterministic differential games where the players are weakly coupled through the state equation and their objective functionals. The weak coupling is characterized in terms of a small perturbation parameter ε. With ε=0, the problem decomposes into two independent standard optimal control problems, while for ε≠0, even though it is possible to derive the necessary and sufficient conditions to be satisfied by a Nash equilibrium solution, it is not always possible to construct such a solution. In this paper, we develop an iterative scheme to obtain an approximate Nash solution when ε lies in a small interval around zero. Further, after requiring strong time consistency and/or robustness of the Nash equilibrium solution when at least one of the players uses dynamic information, we address the issues of existence and uniqueness of these solutions for the cases when both players use the same information, either closed loop or open loop, and when one player uses open-loop information and the other player uses closed-loop information. We also show that, even though the original problem is nonlinear, the higher (than zero) order terms in the Nash equilibria can be obtained as solutions to LQ optimal control problems or static quadratic optimization problems.

Original languageEnglish (US)
Pages (from-to)137-168
Number of pages32
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - Oct 1991


  • Differential games
  • Nash equilibria
  • information structures
  • policy iteration
  • regular perturbation

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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