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Most existing results about last-iterate convergence of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results and techniques that apply to broader families of games and learning dynamics. First, we use a regret-based analysis to show that in a class of games that includes constant-sum polymatrix and strategically zero-sum games, dynamics such as optimistic mirror descentarXiv:2203.12056v1 fatcat:vwlvt2iiqff3ddqlgwhoxscnbu