gametheory101.com/courses/game-theory-101/
Continuity is an axiom of expected utility theory that states for three outcomes X, Y, and Z, where X is preferred to Y is preferred to Z, a probability p exists such that the individual is indifferent between pX + (1 - p)Z and Y. Essentially, some lottery between the best outcome and the worst outcome is equally good as the middle outcome.
Mixed strategies rely on continuity to function properly. Fortunately, most preferences follow continuity---though lexicographic preferences do not.
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