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realized assigns to each state
the probability
if
and the probability zero otherwise
(i.e. the probability of
ω
conditional on
. As an example, if
τ
i
(
ω
) =
ω
for all
then player
i
has full
information about the state of nature. Alternatively, if
and for each player
i
the probability measure
p
i
is
a product measure on
Ω
and
τ
i
(
ω
) =
ω
i
then the players' signals are independent and player
i
does not learn from his
signal anything about the other players' information.
As in a strategic game, each player cares about the action profile; in addition he may care about the state of nature.
Now, even if he knows the action taken by every other player in every state of nature, a player may be uncertain
about the pair (
a
,
ω
) that will be realized given any action that he takes, since he has imperfect information about
the state of nature. Therefore we include in the model a profile
of preference relations over
lotteries
on
A
×
Ω
(where, as before,
). To summarize, we make the following definition.
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This note was uploaded on 09/10/2011 for the course DEFR 090234589 taught by Professor Vinh during the Spring '10 term at Aarhus Universitet, Aarhus.
 Spring '10
 VINH

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