Multicriteria optimization problems of finite horizon stochastic cooperative linear-quadratic difference games

This paper investigates the Pareto optimality of the regular and the indefinite stochastic cooperative linear-quadratic difference games in a finite time horizon. We derive a general form and a linear property of the solution to the linear stochastic difference system by defining several sequences of bounded and linear operators. The performance criteria’s convexity can be guaranteed naturally under the weighted matrices’ constraints for the regular cooperative game, and the weighting technique can well characterize the Pareto optimality. We also establish a novel convexity criterion for the cost functionals of the indefinite cooperative game, in which we find that the minimization of the performance criteria’s weighted sum is equivalent to the Pareto optimal strategies. To derive all the Pareto optimal strategies and solutions, we present a computing algorithm using the weighted difference Riccati equation and the weighted difference Lyapunov equation for the regular and the indefinite cases. We present a practical example in the economy to validate the results.