Bertrand paradox (economics)

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This article is about Bertrand paradox in economics. For Bertrand's paradox related to probability theory, see Bertrand's paradox (probability).

In economics, the Bertrand paradox–so named for its creator, Joseph Bertrand–describes a situation in which two players (companies) reaching a state of Nash equilibrium in economic competition find themselves with no profits.

[edit] Example

Suppose two companies, A and B, sell an identical commodity, each with the same cost of production and distribution, so that customers choose the product solely on the basis of price. It follows that neither A nor B will set a higher price than the other because doing so would yield the entire market to their rival. If they set the same price, the companies will share both the market and profits.

On the other hand, if either company were to lower its price, even a little, it would gain the whole market and substantially larger profits. Since both A and B know this, they will each try to do this, until the product is selling at no profit. This is the Nash equilibrium.

The Bertrand paradox rarely appears in practice because real products are almost always differentiated in some way other than price (brand name, if nothing else); companies have limitations on their capacity to manufacture and distribute; and two companies rarely have identical costs.

Bertrand's result is paradoxical because if the number of firms goes from one to two, the price decreases from the monopoly price to the competitive price and stays at the same level as the number of firms increases further. This is not very realistic, as in the real world, as the number of firms increases the price usually goes down. The empirical analysis shows that in the most industries with two competitors, positive profits are in fact made.

Some reasons the Bertrand paradox does not strictly apply:

• Capacity constraints–Sometimes firms have not enough capacity to satisfy all demand
• Product differentiation–If products of different firms are differentiated, then consumers may not switch completely to the product with lower price
• Dynamic competition–Repeated interaction or repeated price competition can lead to the price above MC in equilibrium.
• More money for higher price–It follows from repeated interaction: If one company sets their price higher slightly then they will still get about the same amount of buys but more profit for each buy, so the other company will higher their price, and so on (only in repeated games, otherwise the price dynamics are in the other direction).

[edit] See also

• Joseph Bertrand
• Bertrand model
• Bertrand equilibrium
• Differentiated Bertrand competition
• Edgeworth paradox
• Efficient rationing

[edit] References

view	Topics in game theory
Definitions	Normal form game · Extensive form game · Cooperative game · Information set · Preference
Equilibrium concepts	Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy
Strategies	Dominant strategies · Mixed strategy · Grim trigger · Tit for Tat
Classes of games	Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design
Games	Prisoner's dilemma · Coordination game · Chicken · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game
Theorems	Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's Theorem
Related topics	Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists