De
fi
nition 200.1:
An
extensive game
consists of the
following components:
1.
The set of players (assumed to be a
fi
nite set),
N
.
2.
A set,
H
, of sequences (histories of actions) satisfying
the following properties:
(2a)
The empty sequence,
∅
, is an element of
H
.
(2b)
If
(
a
k
)
k
=1
,...,K
∈
H
, (where
K
may be in
fi
nity)
and
L < K
, then
(
a
k
)
k
=1
,...,L
∈
H
.
(2c)
If an in
fi
nite sequence,
(
a
k
)
k
=1
,...,
∞
satis
fi
es
(
a
k
)
k
=1
,...,L
∈
H
for every positive integer
L
, then
(
a
k
)
k
=1
,...,
∞
∈
H
.
3.
A function,
P
, that assigns to each non-terminal
history a member of
N
∪
{
c
}
.
(
P
is the player func-
tion, with
P
(
h
)
being the player who takes an action
after the history,
h
.
If
P
(
h
) =
c
holds, then chance or
nature takes the action after the history,
h
.
A history,
(
a
k
)
k
=1
,...,K
, is
terminal
if it is in
fi
nite or if there is no
a
K
+1
such that
(
a
k
)
k
=1
,...,K
+1
∈
H
.)