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Game Theory Rev."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p> This paper deals with [Formula: see text]-person nonzero-sum discrete-time Markov games under a probability criterion, in which the transition probabilities and reward functions are allowed to vary with time. Differing from the existing works on the expected reward criteria, our concern here is to maximize the probabilities that the accumulated rewards until the first passage time to any target set exceed a given goal, which represent the reliability of the players\u2019 income. Under a mild condition, by developing a comparison theorem for the probability criterion, we prove the existence of a Nash equilibrium over history-dependent policies. Moreover, we provide an efficient algorithm for computing [Formula: see text]-Nash equilibria. 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