Nash equilibria of risk-sensitive nonlinear stochastic differential games

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This paper considers a class of risk-sensitive stochastic nonzero-sum differential games with parametrized nonlinear dynamics and parametrized cost functions. The parametrization is such that, if all or some of the parameters are set equal to some nominal values, then the differential game either becomes equivalent to a risk-sensitive stochastic control (RSSC) problem or decouples into several independent RSSC problems, which in turn are equivalent to a class of stochastic zero-sum differential games. This framework allows us to study the sensitivity of the Nash equilibrium (NE) of the original stochastic game to changes in the values of these parameters, and to relate the NE (generally difficult to compute and to establish existence and uniqueness, at least directly) to solutions of RSSC problems, which are relatively easier to obtain. It also allows us to quantify the sensitivity of solutions to RSSC problems (and thereby nonlinear H-control problems) to unmodeled subsystem dynamics controlled by multiple players.

Original languageEnglish (US)
Pages (from-to)479-498
Number of pages20
JournalJournal of Optimization Theory and Applications
Issue number3
StatePublished - Mar 1999


  • Nonlinear H-control
  • Nonzero-sum differential games
  • Perturbation methods
  • Risk-sensitive stochastic control

ASJC Scopus subject areas

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


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