Extensive Form Games
–
Revised item 7
An
extensive form game
is a collection Γ = (
N,A,H,T,ι,
I
,
(
U
i
)
i
∈
N
).
1.
N
, a ﬁnite set of
players
.
2.
A
, a (ﬁnite) set of
actions
.
3.
H
, a (ﬁnite) set of histories (sometimes called nodes), with
(a)
h
0
∈
H
, where
h
0
is the
empty history
.
(b)
h
∈
H
{
h
0
}
only if
h
=
h
0
,a
1
,...,a
k
for some integer
k
≥
1 where
a
‘
∈
A
for
‘
= 1
,...,k
.
(c) For any
k
≥
2, if
h
=
h
0
,a
1
,...,a
k
∈
H
, then
h
=
h
0
,a
1
,...,a
k

1
∈
H
.
4.
A
(
h
) =
{
a
∈
A

(
h,a
)
∈
H
}
is the set of actions available at
h
∈
H
.
5.
T
=
{
h
∈
H

(
h,a
)
/
∈
H
for any
a
∈
A
}
.
T
is the set of
terminal histories
(or
outcomes
).
6. A function
ι
:
H
\
T
→
N
which indicates which player has the move at each nonterminal
history.
7. A partition
I
of
H
\
T
such that for any two members
h,h
0
of the same partition element (i)
A
(
h
) =
A
(
h
0
); (ii)
ι
(
h
) =
ι
(
h
0
). Each element of
I
is an
information set
. For any
h
∈
H
\
T
,
let
I
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 Spring '10
 schlee
 Microeconomics, Game Theory, extensive form, information sets, terminal histories

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