Differential Games of Pursuit

The following sections are included:

• Preface

• Contents

The following sections are included:

• Zero–sum two–person games in normal form

• Equilibrium Point

• Mixed strategies and existence of equilibrium point

• Games with convex payoff function

• One class of games with complete information

• Simultaneous games of pursuit with non–convex payoff functions

The following sections are included:

• Nonformal description

• Game of pursuit in normal form

• Existence of the ε–equilibrium point in differential games with prescribed duration

• Existence of ε–equilibrium points in optimal time differential pursuit games

• Alternative

• Differential games with dependent motions

• Alternative for games with dependent motions and discrimination

The following sections are included:

• Discrete game with terminal payoff and discrimination for player E

• Continuous game without discrimination

• Arbitrary terminal payoff functions and phase constrains

• Optimal time pursuit games

• Necessary and sufficient conditions for existance of optimal open–loop strategy for player E

• Iterative methods for solution of differential game of pursuit

The following sections are included:

• Games with prescribed duration without phase constraints

• Phase–constrained "simple pursuit" games

• "Simple pursuit" game with two pursuers and one evader

• Relations between maximin time of pursuit and time of absorption

The following sections are included:

• Definition of "life line" game

• Discrete game

• Proof of one geometric lemma

• Basic theorem

• Rejection of discrimination

• Multiplayer "life line" games

The following sections are included:

• Pursuit games with delayed information for player P

• Game with information delayed. Case of m pursuiers and one evader

• Existence of equilibria in mixed strategies in "princess and monster" game of pursuit

• Differential games with discrete information partition

• Games with mixed information state

• Pursuit game with prescribed duration and delayed information for both players

• Delayed information for both players when the evader team takes part in game

• One multistage game with delayed information

The following sections are included:

• Game on a finite graph tree

• Nash equilibrium

• Definition of the noncooperative differential games in normal form

• Definition of cooperative differential game in the form of characteristic sets

• Classification of dinamic stable (time – consistant) solutions

• Structure and dynamic stability of pareto optimal solution in the game of approaching

• Existence of dynamic stable C–kernel and NM–solution in cooperative game of approaching

The following sections are included:

• Definition of cooperative differential game in the characteristic function form

• Principle of dynamic stability (time–consistancy)

• Classification of dynamic stable solutions

The following sections are included:

• Integral optimality principles

• Differential strongly time consistent optimality principles

• Strongly time consistent optimality principles for the games with discount payoffs

The following sections are included:

• Bibliography

• Index