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<p>We 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.</p>

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Mather Sets of a Cascade Generated by the FTRL Algorithm of a Two-Agent Zero-Sum Game with Mixed Strategies

  • 期刊论文

  • 发表日期：

    2025年10月28日

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  • Viktoriya Kolner,
  • Ihor Parasyuk

摘要

We 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.