Page 5To model decision-making under uncertainty, almost all game theory uses the theories of von Neumann and Morgenstern (1944) and of Savage (1972). That is, if the consequence function is stochastic and known to the decision-maker (i.e. for each the consequence g(a) is a lottery (probability distribution) on C) then the decision-maker is assumed to behave as if he maximizes the expected value of a (von Neumann-Morgenstern utility) function that attaches a number to each consequence. If the stochastic connection between actions and consequences is not given, the decision-maker is assumed to behave as if he has in mind a (subjective) probability distribution that determines the consequence of any action. In this case the decision-maker is assumed to behave as if he has in mind. a "state space" Ω, a probability measure over Ω, a function , and a utility function ; he is assumed to choose an action a that maximizes the expected value of u(g(a,ω)) with respect to the probability measure.
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