Summary.
We show, by employing a density result for probability measures, that in games with a finite number of players and ∞-dimensional pure strategy spaces Nash equilibria can be approximated by finite mixed strategies. Given ε>0, each player receives an expected utility payoff ε/2 close to his Nash payoff and no player could change his strategy unilaterally and do better than ε.
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Received: July 15, 1997; revised version: February 6, 1998
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Glycopantis, D., Muir, A. Nash equilibria in ∞-dimensional spaces: an approximation theorem. Economic Theory 13, 743–751 (1999). https://doi.org/10.1007/s001990050280
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DOI: https://doi.org/10.1007/s001990050280