An iterative algorithm to solve state-perturbed stochastic algebraic Riccati equations in LQ zero-sum games

An iterative algorithm to solve a kind of state-perturbed stochastic algebraic Riccati equation (SARE) in LQ zero-sum game problems is proposed. In our algorithm, we replace the problem of solving a SARE with an indefinite quadratic term by the problem of solving a sequence of SAREs with a negative semidefinite quadratic term, which can be solved by existing methods. Under some appropriate conditions, we prove that our algorithm is globally convergent. We give a numerical example to show the effectiveness of our algorithm. Our algorithm also has a natural game theoretic interpretation.