David K.H. Begg, Gianluigi Vernasca-Economics-McGraw Hill Higher Education (2011)

CHAPTER 9 Market structure and imperfect competition
Game theory and interdependent decisions
A good poker player sometimes bluffs. You can win with a bad hand if your opponents misread it for
a good hand. Similarly, by having bluffed in the past and been caught, you may persuade opponents to
bet a lot when you have a terrific hand.
A game is a situation in
which intelligent decisions are
necessarily interdependent.
A strategy is a game plan
describing how a player acts,
or moves, in each possible
situation.
In Nash equilibrium, each
player chooses the best strategy,
given the strategies being
followed by other players.
Like poker players, oligopolists try to anticipate their rivals' moves to determine their
own best action. To study interdependent decision making, we use game theory. The
players in the game try to maximize their own payoffs. In an oligopoly, the firms are
the players and their payoffs are their profits in the long run. Each player must choose
a strategy. Being a pickpocket is a strategy. Lifting a particular wallet is a move.
As usual, we are interested in equilibrium. In most games, each player's best
strategy depends on the strategies chosen by other players. It is silly to be a
pickpocket when the police have CCTV cameras or to play four centre backs when
the opponents have no proven goal-scorers.
Nobody, then, wants to change strategy, since other people's strategies are already
figured into assessing each player's best strategy. This definition of equilibrium, and its application to game
theory, was invented by a Princeton University mathematician John Nash. 1
A dominant strategy is a
player's best strategy whatever
the strategies adopted by rivals.
Dominant strategies
Sometimes (but not usually) a player's best strategy is independent of those chosen
by others. We begin with an example in which each player has a dominant strategy.
Figure 9.5 shows a game 2 between the only two members of a cartel. Each firm can
select a high-output or low-output strategy. In each box of Figure 9.5 the orange number shows firm J\s
profits and the blue number firm B's profits for that output combination.
When both have high output, industry output is high, the price is low and each firm makes a small profit
of 1. When each has low output, the outcome is like collusive monopoly. Prices are high and each firm does
better, making a profit of 2. Each firm does best (a profit of 3) when it alone has high output: the other
firm's low output helps hold down industry output and keep up the price. In this situation we assume the
low-output firm makes a profit of 0.
Now we can see how the game will unfold. Consider firm J\s decision. It first thinks what to do if firm B
has a high-output strategy. Firm A will thus be in one of the two left-hand boxes of Figure 9.5. Firm A gets
a profit of 1 by choosing high but a profit of 0 by choosing low. If firm A thinks firm B will choose high
output, firm A prefers high output itself.
But firm A must also think what to do if firm B chooses a low-output strategy. This puts firm A in one of
the two right-hand boxes. Firm A still prefers high output for itself, which yields a profit of 3 whereas low
output yields a profit of only 2. Firm A has a dominant strategy. Whichever strategy B adopts, A does better
to choose a high-output strategy.
1 Nash, who battled schizophrenia, won the Nobel Prize in Economics for his work on game theory. A film about his life, A
Beautiful Mind (dir. Ron Howard), was released in 2001 and starred Russell Crowe.
2 The game, called the Prisoner's Dilemma, was first used to analyse the choice facing two people arrested and in different cells,
each of whom could plead guilty or not guilty to the only crime that had been committed. Each prisoner would plead innocent
if only she knew the other would plead guilty. For more information go to www.mcgraw-hill.co.uk/textbooks/begg where there
is a video fully explaining the Prisoner's Dilemma.
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