Duopoly

Definition

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

A special form of the Cournot Duopoly is the Stackelberg Duopoly

Stackelberg Duopoly

That means that one of the two firms has the first-mover advantage. It is a erweiterung von dem Cournot duopoly. The first mover is called Stackelberg führer and decides about their quantity before the second firm. This one is called Stackelberg folger. The first firm knows that its action is observable by the second firm. Solving by 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??