Hájek's argument establishes that any mixed strategy assigning positive probability to wagering yields infinite expected utility, making dominance reasoning structurally unavailable for resolving mixed-strategy cases.

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Hájek(named as the originator of the argument being discussed): Alan Hájek is a contemporary philosopher who works on probability theory and decision-making. He's known for pointing out logical puzzles that arise when we try to make rational choices.
Positive probability(probability and game theory): A real chance of something happening—more than zero but not necessarily likely.
Structurally unavailable(explains why dominance reasoning fails in these mixed-strategy cases): Impossible to use for fundamental, built-in reasons—not just difficult, but logically ruled out by the nature of the situation itself.
dominance reasoning(game theory): A form of iterative reasoning in game theory where players eliminate dominated actions from consideration, which may reduce the game and render further moves dominated

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