Discrete Stochastic Differential Games

Abstract

Publisher Summary This chapter focuses on discrete stochastic differential games. The term differential games is a derivative of the mathematical theory of games. Games can have many forms depending on the number of players and the way in which winnings and losses are computed. Differential games involve only two players, where the loser pays the winner a specified amount after the play of a given game. As the algebraic sum of the winner's game (positive) and loser's gain (negative) is zero, this type of game is known as two-player zero sum game. Games can be presented either in extensive form as a set of rules and a succession of choices for each player or in normal form as a matrix or function, which relates the amount to the winner to the choices made by the two players. The amount, as a function of the choices, is known as the payoff of the game. An important concept in game theory is information. In games of perfect information, each player knows the exact value of the payoff and all that has occurred in the past. Differential games involve a payoff, which is in some way related to a dynamical system. The two players attempt to optimize this payoff by choosing game optimal control strategies. Differential games can be divided into classes, namely, those where observations of the state are perfect and those where they are not.