In a pursuit evasion game, the pursuer tries to capture the evader while the evader tries to prevent this capture. A classical approach is to model this game as an infinite differential game. In this report, we model a pursuit-evasion game as a finite extensive form game, and show that the differential game is a generalization of this game. We prove that a pure-strategy Nash equilibrium always ...

This paper considers the advertising, pricing, and service decisions simultaneously to coordinate the supply chain with a manufacturer and a retailer. The amount of market demand is influenced by advertising, pricing and service decisions. In this paper, three well-known approaches to the game theory, including the Nash, the Stackelberg-retailer, and the cooperative game are exploited to study ...

Uncertain differential game investigates interactive decision making of players over time and the system dynamics can be described by an uncertain differential equation. This paper goes further to study the two players zero-sum uncertain differential game. In order to guarantee the saddle-point Nash equilibrium, a Max-Min theorem is provided. Furthermore, when the system dynamics is described b...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon. The performance function is assumed to be indefinite and the underlying system affine. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.

As it is well known in differential games, the open-loop Nash equilibrium (OLNE) concept with an infinite period of commitment is weakly time-consistent but not strongly time-consistent. On the other hand, the feedback Nash equilibrium (FBNE) is Markov perfect by construction and thus a more satisfactory solution concept, but solutions are usually very difficult to derive. Explicit solutions ca...

The goal of this paper is to study a stochastic game connected to a system of forward backward stochastic differential equations (FBSDEs) involving delay and noisy memory. We derive sufficient and necessary maximum principles for a set of controls for the players to be a Nash equilibrium in the game. Furthermore, we study a corresponding FBSDE involving Malliavin derivatives. This kind of equat...

To find the possible equilibrium states of forest ecosystems one are suggested to use the theory of differential games. At within the 4-tier model of mosaic forest communities it established the existence of the Nash equilibrium states in such ecosystems. Key–Words: Forest ecosystem, the equilibrium of the ecosystem, differential game, Nash equilibrium October 30, 2016

Nash equilibrium constitutes a central solution concept in game theory. The task of detecting the Nash equilibria of a finite strategic game remains a challenging problem up-to-date. This paper investigates the effectiveness of three computational intelligence techniques, namely, covariance matrix adaptation evolution strategies, particle swarm optimization, as well as, differential evolution, ...