LQ Dynamic Optimization and Differential Games
Chapter One
Introduction
1.1 Historical perspective
Dynamic game theory brings together four features that are key to many situations in
economics, ecology and elsewhere: optimizing behavior, the presence of multiple agents/
players, enduring consequences of decisions and robustness with respect to variability in
the environment.
To deal with problems which have these four features the dynamic game theory
methodology splits the modeling of the problem into three parts. One part is the modeling
of the environment in which the agents act. To obtain a mathematical model of the agents'
environment a set of differential or difference equations is usually specified. These
equations are assumed to capture the main dynamical features of the environment. A
characteristic property of this specification is that these dynamic equations mostly contain
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