A derivation of expected utility maximization in the context of a game
A decision maker faces a decision problem, or a game against nature. For each probability distribution over the state of the world (nature`s strategies), she has a weak order over her acts (pure strategies). We formulate conditions on these weak orders guaranteeing that they can be jointly represented by expected utility maximization with respect to an almost-unique state-dependent utility, that is, a matrix assigning real numbers to act-state pairs.
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