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              <p>We consider infinite antagonistic games over finite graphs. We present conditions that, whenever satisfied by the payoff mapping, assure for both players positional (memoryless) optimal strategies. We show that all popular payoff mappings, such as mean payoff, discounted, parity as well as several other payoffs satisfy these conditions. This approach allows to give a uniform treatment of otherwise disparate results concerning the existence of positional optimal strategies.</p>
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