# Monopolistic Competition and Oligopoly II Game Theory

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Betty
                                                                                                      Paper Scissors Stone
A   0  A -1    A +1
Monopolistic Competition and Oligopoly II:                                                          Paper
B   0  B +1    B -1

Abe
Game Theory                                                                                          A +1   A    0  A -1
Scissors
B -1   B    0  B +1
Keywords:                                                                                                                       A -1   A +1    A    0
Stone
Games                                  Nash equilibrium                                                                         B +1   B -1    B    0
Minimax equilibrium
We are interested in finding out (or predicting) what the outcome will be when
Strategic interaction in economics is the province of game theory, the formal      the game is played. I will go into this in the next example, which is more
analysis of games and economic behavior. We are going to inspect the               relevant to our general discussion.
interaction of firms in an oligopoly using game theory.
We have already dealt with the example of OPEC and oil. Setting up the
A game has three components:                                                       situation as a game, I will show why cartels like OPEC are not stable.
1. Players
2. Strategies                                                                      Suppose we have two players: Iraq and the rest of OPEC1 and they have
3. Payoffs                                                                         signed a cartel agreement which limits each country’s production, thus limiting
overall supply, and hence increasing prices and profits for every country
Every economic (or non-economic) situation involving these components in           involved, since the demand for oil is inelastic.
any form can be modeled as a game.
They have two choices (or strategies): They can either stick to the cartel
To demonstrate the possibilities of game theory, I will first use a non-economic   agreement and produce low, or they can break the cartel agreement and
example:                                                                           produce high.

Consider the game Paper-Scissors-Stone. It is played by two players who            The point that makes this exercise interesting is that if one of them “cheats”
simultaneously choose paper, scissors or stone (their strategy). The winner is     and produces high while the others stick to the agreement, the price will still
determined by the following rules:                                                 be relatively high and the cheater will make much more. For the clarity of the
argument, let us say that each party makes \$20 billion if they stick to the
agreement, the cheater makes \$25 and the honest one \$10 if one of them
 Paper covers stone
cheats, and they both make \$5 if they both cheat (which means lots of oil and
 Stone breaks scissors
very low prices).
 Scissors cut paper.

If both players choose the same thing, the outcome is a draw. These rules
determine the payoffs associated with each outcome. Let 1 denote a win, -1 a
loss, and 0 a draw.
1
All this information can be presented in a very concise and clear manner with       Iraq is just an example, of course. You can take any other country and the rest of OPEC or even any two
countries, it will not change the outcome.
what is called a payoff matrix:
2
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The payoff matrix for this game is as follows:                                                          their Nash strategies coincide is (Cheat, Cheat) and is hence a Nash
equilibrium.
Rest of OPEC (ROO)
Cooperate     Cheat                                          Why is the obviously superior outcome of (Cooperate, Cooperate) not an
Iraq \$20 Iraq      \$5                                       equilibrium in either sense? The reason is that the players both choose to act
Cooperate                                                              in their own best interest and/or do not trust the other. In the case of the
ROO \$20 ROO \$25
Iraq

Iraq \$25 Iraq \$ 10                                          minimax equilibrium, they decide to cheat because they expect the other
Cheat                                                                  player to cheat as well. Under Nash equilibrium, each player thinks that the
ROO      \$5 ROO \$ 10
other player will not respond to his action and chooses to cheat. This is the
The outcome of this game (or its equilibrium) crucially depends on what                                 fundamental reason that cartels such as OPEC are inherently unstable: Most
assumptions we impose on the behavior patterns of the players, or, in more                              of the time, individual players think they can do better by cheating on the
technical terms, what equilibrium concept we choose to use. Two popular                                 agreement.4
ones are the following:
Note that there can be more than one equilibrium in a game or none at all. For
Minimax equilibrium2: An equilibrium at which every player chooses the                                  an example of the former, see Assignment #4, for the latter, see the game of
strategy that yields the highest payoff assuming that the other player(s) will do                       Paper-Scissors-Stone above.5
whatever is worst for the player.                                                                       An important question is whether there is a way for the players to achieve the
more desirable outcome of mutual cooperation? If the game is played as it is
Nash equilibrium: An equilibrium at which every player chooses the strategy                             here, the answer is no. But there are alternatives that make it more likely. One
that yields the highest payoff assuming that the other player(s) do not change                          of them is the case of repeated games. If the game is not a one-shot affair but
their strategies.                                                                                       rather a long term repeated situation, the players might come to realize that
cooperation can be achieved to make them both better off. Analyzing this kind
of situation is extremely complicated because we need to introduce other
The minimax equilibrium of the above game is (Cheat, Cheat). To see that,
concepts like reputation, history and memory.
take Iraq and find what action by ROO will minimize Iraq’s payoff given that
Iraq cooperates (cheat), what action by ROO will minimize Iraq’s payoff given
that Iraq cheats (cheat), and choose the strategy of Iraq that yields the
maximum (cheat). Doing the same for ROO, we find that the equilibrium is
(Cheat, Cheat).3

The Nash equilibrium of the game is also (Cheat, Cheat) but the mechanism
involved in finding it is quite different. When deciding what to do, Nash players
assume that their opponents will stay put and maximize their payoff
accordingly. Thus, assuming that ROO cooperates, Iraq would choose to
cheat. If ROO cheats, Iraq would also choose to cheat. The same argument
goes for ROO since the payoffs involved are identical. The only place where
4
This situation is also called Prisoner’s Dilemma, due to the first presentation of the problem as the decisions
of two criminals who are given the choice of ratting on each other or not cooperating with the police.
5
Technically, every game has a Nash equilibrium, as proven by John Nash in 1951 (he won the Nobel prize
2
Also called maximin equilibrium.                                                                       for his contribution in 1994). The point is that this result also involves mixed strategy equilibria, i.e., those in
3
The behavioral assumption behind this equilibrium concept is that players are pessimistic and try to   which a player plays one strategy with a certain probability and another with another probability, along with
minimize their losses instead of maximizing their gains.                                                the pure strategy equilibria we are looking at.

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