Game theory can help us understand firms interactions

plunk for theory commode help us recognise loadeds interactionsHow can feeble theory help us to netherstand heartys interactions? Discuss the differences between beat and hurt argument.Part I. IntroductionGame theory analysis is a useful tool to study the behaviour of unfluctuatings in oligopolistic grocerys- the fundamental economic problem of controversy between devil or much blind drunks. In this essay I reply think on two of the most notorious frameworks in oligopoly theory Cournot and Bertrand. In the Cournot model, wets control their level of production, which influences the market footing. In the Bertrand model, cockeyeds decide on what price to get along for a unit of product, which affects the market quest. Competition in oligopoly markets is a disciplineting of strategic interaction which is why it is analyzed in a game theoretic context. two Cournot and Bertrand competition atomic number 18 modelled as strategic games. In addition, in both model s a firms revenue is the product of a firms part of the market multiplied by the price. Furthermore, a firm incurs a production apostrophize, which is dependant on its production level. In the simplest model of oligopolistic competition firms play a single game, where actions be taken simultaneously. All firms take in homogenous goods and submit for this good is linear and the cost of production is unyielding per unit. In this market a Nash equaliser in pure strategies exists in both the Cournot and Bertrand models. How constantly, despite the m whatsoever parallels between the models, the Nash equaliser points ar highly different. In Bertrand competition, Nash equilibrium drives prices down to the same level they would be under consummate(a) competition (p=MC), while in Cournot competition, the price at Nash equilibrium is unquestionably higher up the agonistic level.Part II. Cournot and Bertrand CompetitionIn 1838 Augustin Cournot make Recherches sur les Principes Mat hematiques de la Theorie des Richesses, a paper that laid bug out his theories on competition, monopoly, and oligopoly. However Joseph Louis Franois Bertrand concluded that Cournots equilibrium for duopoly firms was not accurate. He went on to argue whatever the common price adopted, if one of the owners, alone, reduces his price, he pass on, ignoring any minor exceptions, attract all of the buyers, and thus double his revenue if his equalise lets him do so.Cournot had originally arrived at his equilibrium by assuming that all(prenominal) firm took the quantity set by its competitors as given, evaluated its residual supplicate and then put its realize maximizing quantity on the market. Here, to all(prenominal) one firms profit work is stated in terms of the quantity set by all other firms. Next, Cournot would partially differentiate each firms profit function with respect to the original firms quantity then set each of the resulting expressions to zero. In the case of a duo poly, Cournot could plot the equations in rectangular coordinates. Here, equilibrium is established where the two curves intersect. By plotting the first order conditions for each firm (i.e. the profit maximizing output of each firm given the quantities set by rivals) Cournot was able to solve for functions that gave the take up reply for each firm depending on the other firms strategies. In game theory this is known as a best repartee function. At the intersection of the best response functions in Cournot competition, each firms assumptions about rival firms strategies are correct. In game theory this is know as a Nash equilibria.Therefore in innovative literature market rivalries based on quantity setting 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 best response functions are referred to Cournot-Nash and Bertrand Nash equilibria consecutively, represe nting a point where no firm can increase profits by unilaterally ever-changing quantity (in the case of Cournot) or price (in the case of Bertrand). The major dispute between Bertrand and Cournot Competition at that placefore lies in how each one determines the competitive process which leads to different mechanisms by which individual consumers demands are allocated by competing firms. That is, Cournot assumes that the market allocates sales equal to what any given firm produces only if at a price determined by what the market will bear, 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 share many characteristics. Both models have the following assumptions that there are many buyers, there are a very small number of major sellers, products are homogenous, there is perfect knowledge, and there is restricted entry. Nonetheless, despite their similarities, their findings pose a utter(a) dichotomy. Under Cournot competition where firms compete by strategically managing their output firms are able to enjoy super-normal profits because the resulting trade price is higher than that of bare(a) cost. On the other hand, under the Bertrand model where firms compete on price, the particular competition is enough to push down prices to the level of marginal cost. The view that a duopoly will lead to the same set of prices as perfect competition is often referred to as the Bertrand paradox.In Bertrand competition, firms 1s optimim price depends on where it moot firm 2 will set its prices. By pricing jus under the other firm it can obtain full market demand (D), while maximizing profits. However if firm 1 expects firm 2 to set price a price that is under marginal cost then the best strategy for firm 1 is to set price higher at marginal cost. In basic terms, firm 1s best response function is p1(p2). This provides firm 1 with the optimal price for ever possible price set by firm 2.The diagram downstairs shows firm 1s reaction function p1(p2), with each firms strategy show on both the axiss. From this we can see that when p2 is less than marginal cost (i.e. firm 2 chooses to price below marginal cost), firm 1 will price at marginal cost (p1=MC). However, when firm 2 prices above marginal cost firm 1 sets price just below that of firm 2.In this model both firms have identical costs. Therefore, firm 2s reaction function is symmetrical to firm 1s with respect to a 45degree line. The result of both firms strategies is a Bertrand Nash equilibrium shown by the intersection of the two reaction functions. This represents a couple up or strategies (in this case price strategies) where neither firm can increase profits by unilaterally changing price.An innate Assumption of the Cournot model is that each firm will aim to increase its profits based on the understanding that its own output decisions will not have an effect on the decisions of its rival firms. In this model price in a commonly know decreasing function of total output. Furthermore, each firm knows N, the total number of firms operating in the market. They take the output of other firms as given. All firms have a cost function ci(qi), which may be the same of different amongst firms. Market price is set at a level so that demand is equal to the total quantity produced by all firms and every firm will take the quantity set by its rivals as a given, evaluate its residual demand, and then behaves a monopoly.Like in Bertrand competition, we can use a best response function to show the quantity that maximizes profit for a firm for every possible quantity produced by the rival firm. We observe a Cournot equilibrium when a quantity pair exists so that both firms are maximizing profits given the quantity produced by the rival.Part III. ConclusionIn reality, neither model is more accurate than the other as there are many different types of industry. In some industries output can be adjusted quickly, thereof Bertrand competition is more accurate at describing firm behaviour. However, if output cannot be adjusted quickly because of fixed production plans (i.e. capacity decisions are do ahead of actual production) then quantity-setting Cournot is more appropriate.