Analyzing games by Boolean matrix iteration

Finite win-draw-lose games with perfect information are studied, using a Boolean formulation with the intention of computational realization. The interdependence of the sets of winning strategies is expressed by means of Boolean matrix equations. Their solutions which describe the winning positions can be obtained by matrix iteration. In the case of last-player-winning games this method shows the existence of two kernels of a bipartite graph which are distinguished in the sense that they bound all other possible kernels. For some chess endings with three and four men all positions are completely analyzed.