Week 5
Repeated games
Ch 14.1-14.6
Repeated interaction
• If players play the same game with the same opponents over and over again we can condition
current actions on the history
◦ If the opponents cooperated in the past we can continue to cooperate and defect otherwise
Prisoners’ dilemma twice
STAGE kid d totalPant att11 8payopattz
Payoff
payoff
t 25,02 whereu fromt
28 u 2 138 payoff
t
Glu
0138,0228 s payoff
Is u
This is a positive a ne transformation, so this sub game is strategically equivalent to the
original stage game, the same applies when t=1
Ui payofffront2 9,4118,11 11
where
Isu12Suez Suiyuan
Dlsu so 2 go sun predicted tobe lil
sthlD.LY
d Iii'ddD
Unraveling
The fact that players play (D, d) no matter the history as it is a unique NE means that as long as T is
nite, cooperation cannot be self-sustained
Inducing cooperation
Multiple equilibria
C
1252112
115
AParetodominates
FIFI D 13 21111111.2 2
Dale311221111
onestepdeviationprinciple
Looking for NE with cooperation: Uls CDisalsa 218 tonotcooperate
incentive
Cc atty Vils DDalseedyB's
incentive tocooperate infirstround
inhistorycc p d isParetoo ptimalNeat 2 oils aDelsale.dz 3 s
inhistoryCdDaDd Dad r
AsthesearebothNEthe subgame isinequilibriumbutmustcheckifneat t as ss set
h oldsitisansene
t his
when
iewhenthe are
p layers p atient
enough
Repeated games
Ch 14.1-14.6
Repeated interaction
• If players play the same game with the same opponents over and over again we can condition
current actions on the history
◦ If the opponents cooperated in the past we can continue to cooperate and defect otherwise
Prisoners’ dilemma twice
STAGE kid d totalPant att11 8payopattz
Payoff
payoff
t 25,02 whereu fromt
28 u 2 138 payoff
t
Glu
0138,0228 s payoff
Is u
This is a positive a ne transformation, so this sub game is strategically equivalent to the
original stage game, the same applies when t=1
Ui payofffront2 9,4118,11 11
where
Isu12Suez Suiyuan
Dlsu so 2 go sun predicted tobe lil
sthlD.LY
d Iii'ddD
Unraveling
The fact that players play (D, d) no matter the history as it is a unique NE means that as long as T is
nite, cooperation cannot be self-sustained
Inducing cooperation
Multiple equilibria
C
1252112
115
AParetodominates
FIFI D 13 21111111.2 2
Dale311221111
onestepdeviationprinciple
Looking for NE with cooperation: Uls CDisalsa 218 tonotcooperate
incentive
Cc atty Vils DDalseedyB's
incentive tocooperate infirstround
inhistorycc p d isParetoo ptimalNeat 2 oils aDelsale.dz 3 s
inhistoryCdDaDd Dad r
AsthesearebothNEthe subgame isinequilibriumbutmustcheckifneat t as ss set
h oldsitisansene
t his
when
iewhenthe are
p layers p atient
enough
