Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies - Kolner, V.; Parasyuk, I. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.9We establish conditions under which a two-dimensional cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies, is determined by a twist mapping of the plane. For the indicated cascade, we prove the existence of Mather sets corresponding to the rotation numbers from a certain interval. In this way, we explain why, in the computer experiments, the orbits of the analyzed cascade are located on closed curves and, in a certain sense, have the property of local convexity.