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To model decisionmaking 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
decisionmaker (i.e. for each
the consequence
g
(
a
) is a lottery (probability distribution) on
C
) then the
decisionmaker is assumed to behave as if he maximizes the expected value of a (
von NeumannMorgenstern
utility
) function that attaches a number to each consequence. If the stochastic connection between actions and
consequences is not given, the decisionmaker 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 decisionmaker 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
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 Spring '10
 VINH

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