Recently, it was shown that Chess-like games may have no uniform(subgame perfect) Nash equilibria in pure positional strategies.\r\nMoreover, Nash equilibria may fail to exist already in two-person games in which all infinite plays are equivalent and ranked as\r\nthe worst outcome by both players. In this paper, we extend this negative result further, providing examples that are uniform Nash\r\nequilibria free, even in mixed or independently mixed strategies.Additionally, in case of independently mixed strategieswe consider\r\ntwo different definitions for effective payoff: the Markovian and the a priori realization.
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