Some thoughts on saddle-point conditions and information structures in zero-sum differential games

For an apparently simple 2-stage linear-quadratic zero-sum difference game with dynamic information structure, we show that (i) there exist nonlinear saddle-point strategies which require the same existence conditions as the well-known linear closed-loop no-memory solution, (ii) there exist both linear and nonlinear saddle-point strategies which require more stringent conditions than the unique open-loop solution. We then discuss the implication of this result on the existence of saddle-points in zero-sum differential games for different information patterns.