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

CHAPTER 9 Market structure and imperfect competition
neither firm wishes to alter its behaviour even after its conjecture about the other firm's output is then
confirmed.
Since both firms face the same industry demand curve, their reaction functions are symmetric if they also
face the same marginal cost curves in Figure 9.6. The two firms then produce the same output Q* as shown
in Figure 9.7. If costs differed, we could still construct (different) reaction functions and their intersection
would no longer imply equal market shares.
Suppose the marginal cost curve of firm A now shifts down in Figure 9.6. At each output assumed for firm
B, firm A now makes more. It moves further down any MR schedule before meeting MC. Hence, in Figure
9.7 the reaction function R A shifts up, showing firm A makes more output Q A at any assumed output Q 13 of
its rival. The new intersection of the reaction functions, say at point F, shows what happens to Nash
equilibrium in the Cournot model.
It is no surprise that the output of firm A rises. Why does the output of firm B fall? With lower marginal
costs, firm A is optimally making more. Unless firm B cuts its output, the price will fall a lot. Firm B prefers
to cut output a little, in order to prop up the price a bit, preventing a big revenue loss on its existing units.
As in our discussion of the Prisoner's Dilemma game in Section 9.4, the Nash-Cournot equilibrium does
not maximize the joint payoffs of the two players. They fail to achieve the total output that maximizes joint
profits. By treating the output of the rival as given, each firm expands too much. Higher output bids down
prices for everybody. In neglecting the fact that its own expansion hurts its rival, each firm's output is too high.
Each firm's behaviour is correct given its assumption that its rival's output is fixed. But expansion by one
firm induces the rival to alter its behaviour. A joint monopolist would take that into account and make
more total profit.
This is considered in Figure 9.8. Suppose there are two identical firms producing cars. The firms have two
possible strategies: co-operate and form a cartel or do not co-operate and compete in quantities. The game
is played simultaneously and only once, so it is a one-shot game. If they co-operate (collude), they can set
the monopoly price and both obtain half of the monopoly profits. If they compete, they both obtain the
Cournot profits, which are lower than in the case of collusion. If a firm is co-operating while the rival
deviates from the collusive agreement, the firm deviating steals most of the market and obtains high profits.
The other firm receives low profits.
From Figure 9.8 we can see that firm A has a dominant strategy (to not co-operate), since that strategy,
independently of what the rival is doing, will provide a payoff of 15 or 5 (co-operating will give firm A
payoffs of 10 or 2). For firm B, we have a dominant strategy as well. Firm B will always choose not to cooperate.
The only Nash equilibrium of the game is to not co-operate for both firms. At that equilibrium,
the firms will get profits of 5, lower than in the case of both co-operating.
In this case, firms do not co-operate because the incentive to deviate from the collusive agreement is large.
By recognizing that, both firms will simply not co-operate and we are back to the Prisoner's Dilemma case.
Firm B
Co-operate
Firm A Co-operate 10, 10
Not co-operate
2, 15
Not co-operate 1 5, 2
5, 5
Figure 9.8
Cournot competition and the Prisoner's Dilemma
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