Nash and Stackelberg solutions to general linear-quadratic two player difference games. I. Open-loop and feedback strategies

Concepts needed in the definition of difference game problems are first studied in detail. Solutions for a general class of deterministic linear quadratic two-player nonzero-sum difference games are then developed. Nash and Stackelberg solutions for open-loop and zero-memory information structure are considered. An augmentation techniques and a dynamic programming approach are applied to obtain the solutions. A recursive algorithm is developed for the Nash open-loop solution. Computational difficulties, which are caused by the augmented representa­ tions when the number of time stages is great, are thus avoided.

[1]  Y. Ho,et al.  Team decision theory and information structures in optimal control problems--Part II , 1972 .

[2]  Y. Ho,et al.  Nonzero-sum differential games , 1969 .

[3]  Jose B. Cruz,et al.  Sampled-data Nash controls in non-zero-sum differential games† , 1973 .

[4]  C. Chen,et al.  Stackelburg solution for two-person games with biased information patterns , 1972 .

[5]  J. Marschak,et al.  Elements for a Theory of Teams , 1955 .

[6]  Jose B. Cruz,et al.  A Stackelberg solution for games with many players , 1973 .

[7]  T. Başar.  Nash strategies for M-person differential games with mixed information structures , 1975, Autom..

[8]  Y. Ho,et al.  Further properties of nonzero-sum differential games , 1969 .

[9]  J. Case,et al.  Toward a theory of many player differential games. , 1969 .

[10]  R. Mukundan,et al.  Linear feedback strategies in non-zero-sum differential games , 1975 .

[11]  R. Radner,et al.  Team Decision Problems , 1962 .

[12]  J. Cruz,et al.  Additional aspects of the Stackelberg strategy in nonzero-sum games , 1973 .

[13]  D. Lukes,et al.  A GLOBAL THEORY FOR LINEAR QUADRATIC DIFFERENTIAL GAMES. , 1971 .

[14]  Z. Rekasius,et al.  On the solution of the optimal linear control problems under conflict of interest , 1971 .

[15]  Jaroslav Dolezal.  Necessary optimality conditions for N-player nonzero-sum multistage games , 1976, Kybernetika.

[16]  Jaroslav Dolezal,et al.  Hierarchical solution concept for static and multistage decision problems with two objectives , 1976, Kybernetika.

[17]  H. Stackelberg,et al.  Marktform und Gleichgewicht , 1935 .

[18]  Y. Ho,et al.  Differential games and optimal pursuit-evasion strategies , 1965 .

[19]  Tamer Baar.  Brief paper: Nash strategies for M-person differential games with mixed information structures , 1975 .

[20]  J. Cruz,et al.  On the Stackelberg strategy in nonzero-sum games , 1973 .

[21]  T. Başar.  A counterexample in linear-quadratic games: Existence of nonlinear nash solutions , 1974 .