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Topological essentiality in infinite games

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  • By constructing a corresponding Nash map, we prove that every infinite game with compact metrizable sets of strategies and continuous payoffs has such a topological essential component that contains a minimal payoff-wise essential set containing a stable set, and deduce that every topological essential equilibrium is payoff-wise essential and so is perfect.
    Mathematics Subject Classification: Primary: 91A10, 60B10; Secondary: 46G12.

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