Strategies for two-player differential games with costly information

In this work, a two players nonzero-sum differential game is considered, where one player tries to minimize some predefined cost and the other tries to maximize the same. The game is described by a stochastic differential system and the actions of the players serve as the control inputs to the dynamical system. The cost being a function of the actions chosen by the players and the state of the dynamical system, the players aim to control the state in order to optimize the cost functional. However in this problem the players do not have the access to the states for every time, rather the states are available at discrete time instances after some finite costs are paid by the players. The inclusion of the information-cost makes the structure of the cost functional non-classical. The work presents the strategies for the players under no-cost information access as well as under costly information access. Explicit time instances for the information access are also derived by solving certain finite dimensional optimization problems.

[1]  W. Fleming,et al.  On the value of stochastic differential games , 2011 .

[2]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[3]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

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

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

[6]  Jacob Engwerda,et al.  LQ Dynamic Optimization and Differential Games , 2005 .

[7]  Tyrone E. Duncan,et al.  Some stochastic differential games with state dependent noise , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[8]  M. R. James,et al.  Partially Observed Differential Games, Infinite-Dimensional Hamilton--Jacobi--Isaacs Equations, and Nonlinear $H_\infty$ Control , 1996 .

[9]  James H. Case.  Equilibrium points of N-person differential games , 1967 .

[10]  Rufus Isaacs,et al.  DIFFERENTIAL GAMES III: THE BASIC PRINCIPLES OF THE SOLUTION PROCESS , 1954 .

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

[12]  S. Z. Alparslan-Gök.  Lecture Notes on Cooperative Game Theory , 2007 .

[13]  J. B. Cruz,et al.  Series Nash solution of two-person, nonzero-sum, linear-quadratic differential games , 1971 .

[14]  T. Başar.  On the uniqueness of the Nash solution in Linear-Quadratic differential Games , 1976 .

[15]  Pierre Bernhard,et al.  Linear-quadratic, two-person, zero-sum differential games: Necessary and sufficient conditions , 1979 .

[16]  A. Weeren,et al.  Asymptotic Analysis of Linear Feedback Nash Equilibria in Nonzero-Sum Linear-Quadratic Differential Games , 1999 .

[17]  W. E. Schmitendorf,et al.  On a class of nonzero-sum, linear-quadratic differential games , 1971 .

[18]  Rhodes,et al.  Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games , 1973 .

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