Chapter 15 (344-350) “Oligopoly price fixing game”
Economist think about oligopoly as a game between a few players, and to
study oligopoly markets they use game theory.
Game Theory- is a set of tools for studying strategic behavior- behavior that
takes into account the expected behavior of others and the recognition of
The Prisoners Dilemma
Art and Bob are caught red-handed stealing a car. Facing airtight cases, they
will receive a sentence of two years each for their crime.
During interviews with the two prisoners, the Crown attorney believes and
suspects that they were involved in a multi million dollar bank robbery, but
this is suspicion.
So he will make the prisoners play a game.
4 parts of a game
o Each prisoner will be placed in separate room and cannot
communicate with the other prisoner. Each are told that they are
suspected of robbing the car.
If they both confess to the larger crime, they will receive a
sentence of 3 years.
If he alone confesses and his accomplice does not, he will
receive only a 1-year sentence while the accomplice receives
o Strategies are all possible actions of each player.
o 2 strategies
Confess to the bank robbery
Deny having committed the bank robbery.
o Since there are 2 players there is 4 possible outcomes.
Art confesses, and bob denies
Bob confesses, Art Denies
o Each prisoner can work his payoff in each of these possible situations,
and we can tabulate the four possible payoffs for each of the prisoners
in what is called a payoff matrix for the game.
o Payoff Matrix- is a table that shows the payoffs for every possible
action by each player for every possible action by each other player.
o Table 15.1 shows the Payoff Matrix between Art and Bob
Outcome o The choices of both players determine the outcome of the game. To
predict the outcome we use an equilibrium idea proposed by John
Nash of Princeton University.
o Nash Equilibrium- Player A takes the best possible action Given the
action of player B and Player B takes the best possible action given the
action of player A.
o In this case Nash equilibrium occurs when Art makes the best choice
given Bobs choice, and when Bob makes the best choice given Art’s
Finding Nash Equilibrium
o Ex- Look at situation from arts view, if Bob confesses, arts best action
is to confess also because its 3 years rather than 10.
o If bob denies, art should confess because its one year rather than 2.
o Now Bobs situation- If art confesses, bob should also confess.
o If art denies, bob should confess since he will only serve one year.
o Dominant-Strategy equilibrium- is an equilibrium in which the best
strategy of each player is to cheat (confess) regardless of the strategy
of the other player.
The dilemma- arises as each prisoner contemplates the consequences of his
decision and puts himself in the place of his accomplice, but each also know
that if he denies it is in the best interest of the other to confess.
Each consider to deny and rely on his accomplice to deny or to confess
hoping that his accomplice denies but expecting him to confess. The dilemma
leads to the equilibrium of the game.
A bad outcome- For prisoners, the equilibrium of the game, with each
confessing is not the best outcome. If neither of them confesses, each only get
2 years for the lesser of crime. There is no better situation since the players
cannot communicate with each other.
Each know if they deny they will serve only 2 years, but that’s not the best
outcome and they must trust each other to deny. This causes a dilemma.
An Oligopoly Price-Fixing Game
o We can use this game theory and a game like the prisoners dilemma to
understand price fixing, price wars and other aspects of firms in the
o We study the specifi