Monday March 12
• Chapter 14 and 15
• To be posted tonight (around midnight)
• Will be due Friday March 21
(Starting with the bottom of page 7 of the notes)
• You will end up with a different result in the prisoner’s dilemma problem
1. You can have a gain that repeats a finite number of times OR
o This will lead to different outcomes (a different Nash equilibrium)
2. The gain can repeat indefinitely into the future
How does repetition affect equilibrium in the Prisoner’s Dilemma problem?
• 1) Originally:
o Both players played once
o The players could not communicate (they could not collude)
o They knew each other’s payoffs (they knew what the other player would
o Result: a non-cooperative Nash equilibrium
Both players were worse off than if they had colluded
• 2) Finite # of Repetitions:
o Same result as we originally had
o We can interact in the first period, and you decide if you want to cheat.
If you cheat in the first period, the other player could potentially
Cheat 5,5 14,1
Cooperate 1,14 10,10
If we played once, both players would cheat
If we played twice, the question is whether we should cheat or not.
Both players have a dominant strategy to cheat After some repetition, they may see that if they both cheat, they’re
worse off (so they should try to cooperate)
If both players cooperate in the first period and Player 1 wants to
punish Player 2, Player 1 can cheat (both would have a dominant
strategy to cheat), but they both do better if they can cooperate
If you assume the other player is still cooperating, you will try to
cheat in the last period.
• Each player knows the other has an incentive to cheat, so to
optimize their profit they will cooperate up until the last
period and then cheat in the end.
o When the repetitions are finite, there will be a cheating equilibrium in
Collusion (cooperation) is not possible.
You can punish the other player by also cheating so that you both
only reach the lower equilibrium
• 3) Infinite # of Repetitions:
o Now we can attain the cooperative equilibrium where we both make higher
profits (shared monopoly/cartel equilibrium)
o We don’t know when the last interaction is going to be
o Two possible punishment strategies players can use to keep the
other player in line:
1) Grim Trigger
• Both players are cooperating as a cartel and getting the
higher shared monopoly profit. One player cheats, and the
other player also cheats indefinitely into the future.
• Each player knows that punishment is possible into the
future. If you give the player a threat that you could cheat all
the way into the future, it deters the other player from
• Not as good as the tit-for-tat strategy
• The problem with this strategy is that you hurt yourself as
well by having lower profits.
• The best solution
• You do what the other player did in the previous period
• Allows you to cooperate again
• If all of a sudden the other player decides to cheat, you
would then cheat in the next period (you both end up at