Game theory research is a useful tool to review the behaviour of firms in oligopolistic marketplaces- the fundamental economic issue of competition between several firms. In this essay I will concentrate on two of the most notorious models in oligopoly theory; Cournot and Bertrand. In the Cournot model, organizations control their level of production, which influences the marketplace price. In the Bertrand model, businesses decide on what price to create for a unit of product, which impacts the marketplace demand. Competition in oligopoly marketplaces is a environment of strategic relationship which is why it is analyzed in a game theoretic context.
Both Cournot and Bertrand competition are modelled as strategic games. Furthermore, in both models a firm's earnings is the product of a organizations area of the market multiplied by the purchase price. Furthermore, a firm incurs a development cost, which is dependant on its development level. In the easiest model of oligopolistic competition firms play a single game, where activities are taken concurrently. All companies produce homogenous goods and demand because of this good is linear and the cost of production is set per device. In this market a Nash equilibrium in real strategies is out there in both Cournot and Bertrand models. However, despite the many parallels between the models, the Nash equilibrium things are extremely different. In Bertrand competition, Nash equilibrium drives prices right down to the same level they might be under perfect competition (p=MC), while in Cournot competition, the purchase price at Nash equilibrium is obviously above the competitive level.
Part II. Cournot and Bertrand Competition
In 1838 Augustin Cournot printed 'Recherches sur les Principes Mathematiques de la Theorie des Richesses', a paper that organized his theories on competition, monopoly, and oligopoly. However Joseph Louis Franois Bertrand concluded that Cournots equilibrium for duopoly organizations was not exact. He continued to argue 'whatever the common price implemented, if one of the owners, only, reduces his price, he will, ignoring any minor exceptions, attract all of the buyers, and therefore double his revenue if his rival enables him do so'.
Cournot had actually arrived at his equilibrium by let's assume that each firm needed the quantity established by its rivals as given, examined its residual demand and then put its revenue maximizing quantity on the marketplace. Here, each firms revenue function is explained in conditions of the quantity set by all other firms. Next, Cournot would partly differentiate each companies profit function with respect to the original firms number then set each one of the causing expressions to zero. Regarding a duopoly, Cournot could plot the equations in rectangular coordinates. Here, equilibrium is set up where the two curves intersect. By plotting the first order conditions for each and every company (i. e. the income maximizing output of every organization given the volumes set by rivals) Cournot was able to solve for functions that gave the best reaction for each firm depending on the other firms' strategies. In game theory this is actually a 'best response function'. At the intersection of the greatest response functions in Cournot competition, each firm's assumptions about rival firm's strategies are accurate. In game theory this is know as a Nash equilibria.
Therefore in modern literature market rivalries based on quantity setting up strategies are referred to 'Cournot competition' whereas rivalries based on price strategies are referred to as 'Bertrand competition. ' In each model, the intersections of the greatest response functions are referred to 'Cournot-Nash' and 'Bertrand Nash' equilibria consecutively, representing a spot where no firm can increase gains by unilaterally changing number (in the case of Cournot) or price (in the case of Bertrand). The major discord between Bertrand and Cournot Competition therefore is based on how each one can determine the competitive process which causes different mechanisms by which individual consumers' needs are allocated by contending firms. That is, Cournot assumes that the marketplace allocates sales add up to what any given organization produces but at a cost dependant on what the marketplace will carry, but Bertrand assumes that the firm with the lowest price is allocated all sales.
Being that Bertrand Competition and Cournot competition are both models of oligopolistic market structures, they both discuss many characteristics. Both models have the following assumptions; that there are many buyers, there are always a very small variety of major vendors, products are homogenous, there is perfect knowledge, and there is restricted access. Nonetheless, despite their similarities, their results pose a stark dichotomy. Under Cournot competition where firms contend by strategically managing their output firms are able to enjoy super-normal revenue because the causing Selling price is greater than that of marginal cost. Alternatively, under the Bertrand model where companies remain competitive on price, the limited competition is enough to drive down prices to the level of marginal cost. The idea that a duopoly will lead to the same group of prices as perfect competition is also known as the 'Bertrand paradox. '
In Bertrand competition, organizations 1's optimim price depends upon where it believe that company 2 will arranged its prices. By rates jus below the other organization it can obtain full market demand (D), while increasing earnings. However if organization 1 expects firm 2 to set price a cost that is below marginal cost then your best strategy for firm 1 is to set price higher at marginal cost. In basic terms, company 1's best response function is p1"(p2). This gives firm 1 with the perfect price permanently possible price established by company 2.
The diagram below shows organization 1's response function p1"(p2), with each firms strategy show on both axis's. From this we can see that whenever p2 is less than marginal cost (i. e. company 2 decides to price below marginal cost), company 1 will price at marginal cost (p1=MC). However, when firm 2 prices above marginal cost company 1 models price just underneath that of company 2.
In this model both businesses have indistinguishable costs. Therefore, company 2's reaction function is symmetrical to firm 1's with respect to a 45degree line. The result of both businesses strategies is a 'Bertrand Nash equilibrium' shown by the intersection of both response functions. This signifies a pair or strategies (in cases like this price strategies) where neither company can increase earnings by unilaterally changing price.
An essential Assumption of the Cournot model is that every firm will aim to maximize its earnings predicated on the knowing that its own result decisions will not have an impact on the decisions of its rival businesses. Within this model price in a commonly know lowering function of total outcome. Furthermore, each firm knows N, the total number of organizations operating in the market. They take the end result of other firms as given. All firms have a cost function ci(qi), which might be the same of different amidst firms. Market price is set at a level so that demand is equal to the total amount made by all businesses and every firm will take the number established by its rivals as confirmed, evaluate its residual demand, and then behaves a monopoly.
Like in Bertrand competition, we may use a best response function to show the number that maximizes income for a company for each possible quantity produced by the rival company. We view a Cournot equilibrium when a quantity pair exists so that both firms are maximizing revenue given the number produced by the competitor.
Part III. Conclusion
In actuality, neither model is 'more correct' than the other as there are various types of industry. In a few industries productivity can be fine-tuned quickly, therefore Bertrand competition is more exact at describing firm behaviour. However, if output cannot be modified quickly because of preset production ideas (i. e. capacity decisions are created ahead of genuine creation) then quantity-setting Cournot is more appropriate.
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