Department of Economics and Finance
Dr. Chris Dumas
Recall the example game "Cola Wars" from the Game Theory 1 handout.
"Cola Wars" is a simultaneous
move game in which each player has a dominant strategy, namely "Sale," and the outcome of the game is a
"Prisoners' Dilemma" in which the players find themselves in the dominant strategy equilibrium (Coke
plays "Sale," Pepsi plays "Sale").
This equilibrium is undesirable form the players' perspective, they would
prefer to be in the "High Price" / "High Price" equilibrium.
Common sense suggests that cooperation
between the players would arise over time if the players played this game repeatedly with one another.
Suppose the "Cola Wars" game is played for a finite (fixed) number of repetitions.
Each turn, one of the
players says to the other, "Hey, let's cooperate and set high prices.
If either one of us cheats, the other can
punish him by choosing Sale prices forever."
(This is illegal, but suppose they have some way to
communicate and not get caught.)
Would this offer be credible?
Well, on the last turn of the game, it
would not be credible, because on the last turn of the game there are no future turns on which to punish a
cheating player, and the game reverts to the simple one-shot "Cola Wars" game described above, in which
each player plays his dominant strategy, "Sale."
On the next-to-last turn of the game, one player says to the
other "Hey, let's cooperate and set high prices.
If either one of us cheats, the other can punish him on the
last turn by choosing the Sale price."
Now, the other player knows that both players will choose "Sale" on
the last turn, so there is no way to "punish" a player who cheats in the next-to-last turn, because both
players know that they are both going to play "Sale"on the last turn anyway, regardless of what happens in