Recursive Solution Methodology
•
Abreu, D., D. Pearce, and E. Stacchetti (1990), “Toward a Theory of
Discounted Repeated Games with Imperfect Monitoring,”
Econometrica
,
58, 104163.
1
Environment
1.1
Stage Game
•
N
player stage game denoted
G.
•
Each player
i
has a
f
nite strategy set
S
i
and payo
f
function
Π
i
:
S
→
R
where
S
=
S
1
×
...
×
S
N
.
•
For
q
∈
S,
Π
i
(
q
) is an expected value.
•
Realization or payo
f
actually received is stochastic and denoted
π
i
(
p, q
i
)
depending on realization of random variable
P
which takes values
p
∈
Ω
.
•
Distribution of
P
given by
Ψ
(
·
;
q
)
.
•
Realized payo
f
s
π
i
depend on
q
−
i
=(
q
1
, ..., q
i
−
1
,q
i
+1
, ..., q
N
) only through
their e
f
ect on only
Ψ
.
•
Π
i
(
q
)=
R
Ω
π
i
(
p, q
i
)
Ψ
(
dp
;
q
)
.
1.2
Repeated Game
•
G
∞
(
δ
)denotesthein
f
nitely repeated game with stage game
G
and dis
count factor
δ
∈
(0
,
1)
.
•
Let
p
t
and
q
t
denote
t
period signal and action histories.
•
Information Structure: Players can observe (and therefore condition on)
only their own past actions
q
t
i
and past realizations of
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 Spring '07
 CORBAE
 Game Theory, stage game, Si Si, admissable wrt, monotonically decreasing sets

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