Duopoly

A duopoly Is a special form of an oligopoly, a market form. The assumptions are that u have two firms that sell their product to a large number of customers. They produce a homogeneous good at constant marginal costs without any fixed costs. Always try to find a nash equilibrium. That means that the action of one player is an optimal response to the other player's strategy. If the equilibrium is reached, no one of the participants wants to deviate. Both firms want to maximize their profit.

You can differentiate between two Duopolys: You can compete in quantity or price: Cournot Duopoly or Bertrand Duopoly.

Cournot Duopoly

If you compete in quantities then it is called a Cournot duopoly. The price determines by the demand function. Both firms choose the quantity that they want to produce. The payoff of each firm depends on this decision. The nash equilibrium is permitted through the solution of the reaction functions of both firms. Springer

Stackelberg Duopoly

A special form of the Cournot Duopoly is the Stackelberg Duopoly. It is an extension erweiterung of the Cournot duopoly. That means that one of the two firms has the first-mover advantage. The first mover is called Stackelberg leader and decides about their quantity before the second firm. This one is called Stackelberg follower. The first firm knows that its action is observable by the second firm. For getting a solution by calculation you use a backward induction.

Bertrand Duopoly

Bertrand invented a new kind of duopoly. The assumption is that firms use the quantity as a strategic variable and therefore adapt the price. If the firms compete in directly in prices the name is Bertrand competition. The Strategy is that both firms choose their price simultaneously. The clients buy where the price is lower. The only possible equilibrium is if both prices p1 and p2 and the fixed costs are the same. But consequently, it leads to losses while a higher price leads to profits of zero. This is known as the Bertrand paradox. Springer

Literature shows ways out of Bertrand's paradox: for example asymmetric marginal costs or switching costs. Springer??

Comparison of the duopolys

If you compare those two kind of duopoly possibilities there are some important issues.

• Bertrand vs Cournot

1. Cournot profits are strictly positive.
2. Fixed costs have no impact only if the equilibrium profit would be negative
3. higher marginal costs do not affect the profit of zero
4. quantities and profits decrease in the number of competing firms

Profits, the overall surplus are higher in Cournot when the goods are substitutes. If the goods are independent, then the profits are equal. Duopoly information equilibrium

• Stackelberg vs Cournot

In the Stackelberg case the first mover has an advantage. The leader receives a higher profit than the follower.

Exampels in the Economy

One of the most known examples in real life is the competition between the companies Airbus and Boeing. Because of the high amount of orders there's no need to lower the costs. It approaches the Cournot price. The question is if there's not enough competition which impact has it on the clients. The two firms can hold the prices very high. For such possible collaborations, there are authorities to control the behavior of the companies.

Luftfahrtindustrie: problematisches duopol

References

• Röhl K. (2018) [1] "Luftfahrtindustrie: Problematisches Duopol", Institut der deutschen Wirtschaft (IW), Köln

Author: Annamarie Dietz