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Game theory can help us understand organizations interactions

How can game theory help us to understand firms' interactions? Discuss the dissimilarities between quantity and price competition.

Part I. Introduction

Game theory analysis is a good tool to review the behaviour of firms in oligopolistic markets- the fundamental economic problem of competition between several firms. In this article I will concentrate on two of the very most notorious models in oligopoly theory; Cournot and Bertrand. Within the Cournot model, organizations control their level of production, which influences the marketplace price. Within the Bertrand model, organizations decide on what price to create for a unit of product, which affects the market demand. Competition in oligopoly markets is a setting of strategic interaction which explains why it is analyzed in a casino game theoretic context.

Both Cournot and Bertrand competition are modelled as strategic games. In addition, in both models a firm's revenue is the merchandise of a firms area of the market multiplied by the purchase price. Furthermore, a company incurs a production cost, which will depend on its production level. In the easiest style of oligopolistic competition firms play a single game, where actions are taken simultaneously. All businesses produce homogenous goods and demand for this good is linear and the expense of production is fixed per unit. In this market a Nash equilibrium in pure strategies exists in both the Cournot and Bertrand models. However, regardless of the many parallels between the models, the Nash equilibrium points are extremely different. In Bertrand competition, Nash equilibrium drives prices 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 published '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 firms was not accurate. He went on to argue 'whatever the normal price adopted, if one of the owners, alone, reduces his price, he'll, ignoring any minor exceptions, attract all of the buyers, and thus double his income if his rival lets him do so'.

Cournot had actually arrived at his equilibrium by let's assume that each firm took the quantity set by its opponents as given, evaluated its residual demand and then put its profit maximizing quantity on the marketplace. Here, each organizations profit function is explained in conditions of the quantity set by all the firms. Next, Cournot would partially differentiate each organizations profit function with regards to the original firms quantity then set each one of the resulting expressions to zero. Regarding a duopoly, Cournot could plot the equations in rectangular coordinates. Here, equilibrium is made where in fact the two curves intersect. By plotting the first order conditions for each and every 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 best reaction for every single firm with respect to the other firms' strategies. In game theory this is actually a 'best response function'. In the intersection of the best response functions in Cournot competition, each firm's assumptions about rival firm's strategies are correct. In game theory this is know as a Nash equilibria.

Therefore in modern 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 greatest response functions are described 'Cournot-Nash' and 'Bertrand Nash' equilibria consecutively, representing a point where no firm can increase profits by unilaterally changing quantity (in the case of Cournot) or price (in the case of Bertrand). The major conflict between Bertrand and Cournot Competition therefore lies in how each one determines the competitive process which brings about different mechanisms where individual consumers' demands are allocated by competing firms. That is, Cournot assumes that the market allocates sales add up to what any given firm produces but at a price determined by what the marketplace 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 we now have many buyers, there are always a very small volume of major sellers, products are homogenous, there is perfect knowledge, and there is restricted entry. Nonetheless, despite their similarities, their findings pose a stark dichotomy. Under Cournot competition where firms compete by strategically managing their output firms have the ability to enjoy super-normal profits because the resulting Market price is greater than that of marginal cost. Alternatively, under the Bertrand model where companies compete on price, the limited competition is enough to push down prices to the amount of marginal cost. The idea 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, businesses 1's optimim price depends on where it believe firm 2 will set its prices. By pricing jus below the other firm it can buy full market demand (D), while maximizing profits. However if firm 1 expects firm 2 to create price a cost that is below marginal cost then your best strategy for firm 1 is to create price higher at marginal cost. In basic terms, firm 1's best response function is p1"(p2). This gives firm 1 with the optimal price for ever possible price set by firm 2.

The diagram below shows firm 1's reaction function p1"(p2), with each businesses strategy show on both the axis's. From this we can easily see that whenever 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 underneath that of firm 2.

In this model both organizations have identical costs. Therefore, firm 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 reaction functions. This represents a couple or strategies (in cases like this price strategies) where neither firm can increase profits by unilaterally changing price.

An essential Assumption of the Cournot model is that all firm will try to maximize its profits predicated on the understanding that its output decisions will not have an impact on the decisions of its rival firms. In such a model price in a commonly know decreasing function of total output. Furthermore, each firm knows N, the total number of organizations operating on the market. They take the output of other organizations as given. All organizations have an expense function ci(qi), which may be the same of different among firms. Selling price is set at a level so that demand is add up to the total quantity made by all businesses and every firm will need the quantity set 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 showing the number that maximizes profit for a company for each possible quantity produced by the rival firm. We observe a Cournot equilibrium whenever a quantity pair exists so that both companies are maximizing profits given the number produced by the rival.

Part III. Conclusion

In reality, neither model is 'more accurate' than the other as there are many different types of industry. In a few industries output can be adjusted quickly, therefore Bertrand competition is more accurate at describing firm behaviour. However, if output can't be adjusted quickly because of fixed production plans (i. e. capacity decisions are made before actual production) then quantity-setting Cournot is appropriate.

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