This recognition allows the sophisticated duopolist to determine the reaction curve of his rival and incorporate it in his own profit function, which he then proceeds to maximise like a monopolist. The following essay evaluates the usefulness of the Stackelberg Model in explaining the behavior the firms in oligopolistic markets. It shows clearly that naive behaviour does not pay. The extension to n-player model has been tested for different market conditions both, where the information is perfectly interracted amongst all players, and where there is uncertainty and incomplete information. Finally, if both duopolists want to be leaders a disequilibrium arises, whose outcome, according to Stackelberg, is economic warfare.
Firm A is the leader firm, and B the follower one. In fact, its best response by the definition of Cournot equilibrium is to play Cournot quantity. Specifically, Cournot constructed profit functions for each firm, and then used to construct a function representing a firm's for given exogenous output levels of the other firm s in the market. The model has been increasingly used in many industries across the world to explain the behavior of the firms in oligopoly. Indeed, if the 'follower' could commit to a Stackelberg leader action and the 'leader' knew this, the leader's best response would be to play a Stackelberg follower action. Diagram 2 shows both reaction functions.
Lastly, Cournot competition is widely seen in many oligopoly markets and a prime example is the aircraft industry where there are initially high set up costs and only two providers, Airbus and Boeing. Therefore, while determining his optimal output, he would recognise the influence that he would exert on the follower. In Cournot competition, it is the simultaneity of the game the imperfection of knowledge that results in neither player being at a disadvantage. This is an example of too much information hurting a player. To find the of the game we need to use backward induction, as in any sequential game. The model is solved by.
The leader then picks a quantity that maximises its payoff, anticipating the predicted response of the follower. This is unlikely to be the case in a practical sense. Note that the Bertrand equilibrium is a weak Nash-equilibrium. That is why, at any particular q A output of firm A , firm B will produce that output q B at which the ordinate at q A would become a tangent to an iso-profit curve of B. In other words, each duopolist conjectures that his rival is an output-follower and he is an output-leader. Coca-Cola and Pepsi are examples of Bertrand duopolists. Let us now suppose that the market demand function for the product and the cost functions of the duopolists are: Comparison between the Cournot Solution and the Quasi-Competitive Solution: We may now compare the Cournot solution 14.
The basic version of the model dealt with a , or two main producers in a market. The leader is, however, in no danger. If price is equal to unit cost, then it is indifferent to how much it sells, since it earns no profit. A similar process will repeat itself until the stable equilibrium level of is reached. Each duopolist estimates the maximum profit that he would earn a if he acted as leader, b if he acted as follower, and chooses the behaviour which yields the largest maximum. It would be irrational to price below marginal cost because the firm would make a loss.
The Stackelberg Disequilibrium : In this model, we shall suppose that both the duopolists are striving to be the output leader. In this model, each duopolist determines his maximum profit level from both leadership and followership and desires to play the role which yields the larger maximum. Bertrand competition is a model of competition used in economics, named after 1822—1900. As we have seen, case i results in a determinate equilibrium. Stackelberg and Cournot equilibria are stable in a static model of just one period.
If output and capacity are difficult to adjust, then Cournot is generally a better model. A leader does not obey his own reaction function. This profile is a Nash equilibrium. This recognition will permit firm A to choose to set its own output at the level which maximizes its own profit. Hence, such a threat by the follower would not be credible. The profit-maximisation problem of the leader may be analysed, therefore, in the following way. We may now obtain the Cournot solution for the market model given by equations 14.
This quantity is decided keeping in mind mind the expected answer of the follower. We may also note that if the duopolists are not satisfied with the present position, then each of them may seek to alter it to his advantage. Instead, he simply assumes that the duopolists are aware of their interdependence. In the Cournot model, however, there is no scope for price competition since here the duopolists are price-takers. There are at least two firms producing a homogeneous undifferentiated product and cannot cooperate in any way. Four cases are possible here: i A desires to be a leader, and B a follower; ii B desires to be a leader, and A a follower; iii Both desire to be followers; and iv Both desire to be leaders.
The equilibrium solution of the Cournot model, as we already know, is obtained at the point of intersection of the two reaction functions. In this model, A will first start with the monopolistic price; B then enters the market, reducing the price somewhat, and captures the whole market. After all, the quantity chosen by the leader in equilibrium is only optimal if the follower also plays in equilibrium. If it can observe, it will so that it can make the optimal decision. We may illustrate the consequences of these assumptions with the help of Fig. Some of these iso-profit curves have been drawn in Fig.