Beschreibung:
This chapter discusses the differential games economic applications. Much of the application of N-person, general-sum differential games is in economics, where observed regularities are rarely invariant as in natural sciences. Thus, expenditure patterns in America offer little insights upon the consumption habits in Papua-New Guinea. Out of those differential games that depend on specific function forms (e.g., the linear-quadratic game), useful theoretic examples may be constructed but not the basis for robust predictions. In the case of optimal control, broad conclusions are often obtained by means of the globally analytic phase diagram for those problems with a low-dimension state space. On the other hand, from the viewpoint of economics, there are two distinct types of contributions that differential games can offer. First is regarding the multiplicity of solutions: differential game can yield broad conceptual contributions that do not require the detailed solution(s) of a particular game. Second, there remains an unsatisfied need that differential games may meet. For situations where a single decision maker faces an impersonal environment, the system dynamics can be studied fruitfully with optimal control models. There are analogous situations where the system dynamics is decided by the interactions of a few players. Differential games seem to be the natural tool. What economists wish to predict is not only the details about a single time profile, such as existence and stability of any long run configuration and the monotonicity and speed of convergence toward that limit, but also the findings from the sensitivity analysis: how such a configuration responds to parametric variations.