Stochastic differential games. Theory and applications
This book is a kind of survey of what is known in the literature on stochastic differential games. Thus we can think of conflict situations involving two or more players assuming that the movement or the behavior of each player is described by a stochastic differential equation (SDE). Different kind of games are considered such as zero-sum games, pursuit-evasion games and \(N\)-person noncooperative games. In any of the models the payoff function and the sets of controls for the players are specified in one or another way. Because of the complexity of the models, it is not easy to find the value of the game and the optimal strategies of the players. Better studied are cases when linear SDEs govern the behavior of the players, in particular in two-player games. Approximate procedures and convergence results are described. Other aspects are also discussed, e.g. the role of the information available to the players and the type of strategies to use. The authors suggest that some results and ideas in stochastic differential games can be used in the financial business.
scientific article; zbMATH DE number 5996334