Lecture Notes on Non-Cooperative Game Theory
نویسنده
چکیده
We consider in this paper a class of risk-sensitive stochastic nonzero-sum differential games with parameterized nonlinear dynamics and parameterized 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 (which is generally difficult to compute, and establish existence and uniqueness for – 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 to nonlinear H∞-control problems) to unmodelled subsystem dynamics controlled by multiple players.
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