Abstract
Uncertainty theory provides us an alternative for modeling human uncertainty without the scope of probability theory. In a dynamic game, the system dynamics often has noise by human disturbance and can be described by an uncertain differential equation. In order to investigate such a problem, an uncertain differential game model and its solution concept of feedback Nash equilibrium is proposed in this paper. Moreover, a sufficient condition is established to guarantee a feedback Nash equilibrium of the game. As an application, the capitalism problem is analyzed by uncertain differential game. The results show that uncertain differential game is a powerful tool for dealing with dynamic game.
Highlights
As a collection of mathematical models of conflict and cooperation between rational decision makers, game theory [1] has been proven useful in many fields such as economics, management science, and sociology
When the system state is continuous over time and the system dynamics can be described by a differential equation, dynamic game has evolved into the differential game
The government will tax less than the full amount of the payoff accrued to the firm, which will post a positive rate of investment
Summary
As a collection of mathematical models of conflict and cooperation between rational decision makers, game theory [1] has been proven useful in many fields such as economics, management science, and sociology. The origin of differential game could be traced to the pioneering work of Rufus Isaacs, who modeled missile versus enemy aircraft pursuit schemes in terms of state and control variables. His famous book Differential Games [3] marked the birth of the differential game. Much further work springed up in the field of differential game. In 1971, Friedman [7] introduced discrete approximation sequence methods to establish the values of differential game and existence of saddle point. His work laid a solid mathematical foundation for differential game theory
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