| Research Abstract |
Dynamic games deal with situations in which the fortunes of the agents, in some way or another, are interdependent over time. In management sciences, interdependence is a central theme, too. Managers need to deal with interdependence between the firm and its competitors, between the firm and the consumers in a market, between the firm and its suppliers, between the individual and groups within the organization and between the firm and the government regulator agencies.
In this paper, we first study some theoretical aspects of dynamic game in robust control problems, which include 1) the nonstandard extension of the H infinite control problem for singularly perturbed system, 2) the recursive approach to solve the H infinite control problem for singularly perturbed system under both perfect- and imperfect-state measures, 3) the recursive algorithm for mixed H2 and H infinite control problem of singularly perturbed systems. We then have studied the linear quadratic zero-sum dynamic games for descriptor systems and the solution of the generalized differential Riccati equations. A new algorithm for solving the cross-coupled algebraic Riccati equation arising in Nash game of singularly perturbed systems is also proposed.
Finally, as the application of dynamic game in management sciences, we have studied the oligopoly market competition of several firms. We have constructed a game model, which is based on Lancheter Model, in business education. Students have extended the model successfully to their own field in business.
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