Bertrand competition

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The Bertrand competition was developed as a model by Joseph Bertrand for the competition form of the oligopoly in its simplest form as a duopoly . It is a further development of the Cournot oligopoly . The main difference is that the price and not the quantity is used as a strategic variable set simultaneously by the companies; it is therefore a price competition .

Bertrand model of price competition

In a market with a homogeneous good (e.g. water) there are two suppliers (A and B) ( duopoly ). These providers only compete by simultaneously announcing the price. All consumers only buy from the provider with the lowest price. This provider can then satisfy the entire demand . If both companies offer the same price, they share the market , i. H. 50% of consumers go to provider A, the rest to provider B. The fixed costs are negligible and marginal costs are constant, so marginal costs = average costs .

Game theory consideration

From a game theory point of view, the Bertrand competition is based on the idea that both providers act strategically through prices. If both providers act according to this maxim, a Nash equilibrium is achieved for both companies, both ultimately bid at their marginal costs . Because both companies will - fictitiously - undercut each other until the marginal cost price is reached. A response is always necessary as the one with the lower price would draw all the demand . No more reaction is necessary or possible when price = marginal costs is reached. The offer price corresponds to the competition price.

The Nash equilibrium does not result in the long term, but immediately. Both companies will mentally anticipate the competitor's response to their own actions. Your own actions would be thought through until the competitor's best answer corresponds exactly to the intended action. This means that there is no incentive for any of the players to leave the Nash equilibrium.

Every company knows that it would make zero profits if it set a price above marginal costs, because it can already imagine that the competitor would marginally undercut the set price. Setting prices above marginal costs is therefore not sensible (one makes zero profits, the competitor makes profits), and it is also not rational to set a price below marginal costs, because that leads to losses (or at best to zero profits, if the competitor - for whatever reason - undercutting its own price again). The only price setting that doesn't turn out to be wrong in retrospect is to set the price equal to the marginal cost.

Balance in the Bertrand competition

claim

There is a clear Nash equilibrium in which:

( Marginal cost ).

The premise is assumed that both companies have the same cost structure with the same, constant marginal costs (the case is described below if this premise is not met).

proof

There are four options for price selection for provider A:

  1. The price is below the marginal cost of its own company: the company makes a loss on every unit sold, so this cannot happen, instead the provider will raise the price or leave the market.
  2. The price is both above the marginal costs and above the price of provider B: All consumers are supplied by provider B, provider A cannot achieve any sales at this price and will not continue to offer at this price.
  3. The price of provider A corresponds to that of provider B and is above the marginal costs: Both companies share the market in a ratio of 1: 1. Although provider A makes a profit here, it is still not a stable equilibrium in the sense of the Nash equilibrium, because if one of the two providers deviates from the equilibrium and reduces the price, this can, as in case (2), the entire Serving the market and thereby increasing profit while the other provider again fails to achieve sales.
  4. The price of provider A corresponds to that of provider B and is at the level of the marginal costs: In contrast to case (3), there is a stable equilibrium here, since no provider can deviate from it, because the provider cannot do better through a price reduction or price increase put. Therefore, this is the only solution for the price selection, this also applies analogously to provider B and it is therefore a Nash equilibrium.

Bertrand paradox

The Bertrand paradox found by Bertrand with this result describes a state in which two providers are in a situation in which they are not making a profit because neither of the two has market power. This initially implausible result is based on the infinitely great price elasticity of the demand for a homogeneous good.

It must be taken into account that, as with all game theory representations, this is a model that cannot claim (and does not claim) to depict real reality, but rather abstracts from various aspects of reality. On the demand side, it is assumed that the provider can be changed at any time and effortlessly and that it takes place rationally, i.e. factors such as brand image, marketing, habits etc. play no role. Perfect information is a prerequisite for both supply and demand. And finally, on the supply side, fixed marginal costs are assumed, while in reality neither the rate of surplus value nor productivity are static. What the model does is to emphasize the relevance of these additional requirements.

Different marginal costs

In the case of different marginal costs, the position of the cheapest supplier is comparable to that of the supplier in a monopoly , since it combines all of the market demand. However, it has no monopoly power; on the contrary, the market position is constantly contestable, for example by a new competitor with even lower marginal costs. In this case, all market demand would be lost immediately. The lack of market power (and the resulting impossibility to achieve monopoly profits) can result in a Pareto-optimal situation .

literature

Primary literature

  • Léon Walras 1883: Théorie Mathématique de la Richesse Sociale. Journal des Savants, pp. 499-508.

Secondary literature

  • Hal Varian , Grundzüge der Mikroökonomik, 5th edition, Munich 2001, ISBN 3486255436 , there p. 467 ff. (Section 27.9)
  • Ulrich Fehl, Peter Oberender, Fundamentals of Microeconomics, 7th edition, ISBN 3800628481 , p. 69 ff.
  • Wilhelm Pfähler / Harald Wiese: Corporate strategies in competition - A game-theoretical analysis, Springer Verlag, Heidelberg, second edition 2006, ISBN 3-540-28000-6 .
  • Alexander F. Tieman / Gerard van der Laan / Harold Houba: Bertrand Price Competition in a social environment , in: De Economist 149 (2001), pp. 33-51.

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