There is another, different, Bertrand's paradox related to probability; see Bertrand's paradox (probability). This article is about Bertrand's paradox in economics.

In economics, the Bertrand paradox describes a situation in which two players reaching a state of Nash equilibrium find themselves with no profits.

Example

Suppose two companies, A and B, sell an identical commodity product, each with the same cost of production and distribution, and that customers choose the product solely on the basis of price. 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.

But 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, companies have limitations on their capacity to manufacture and distribute, and two companies rarely have identical costs.