In economics and commerce, the Bertrand paradox — named after its creator, Joseph Bertrand[1] — describes a situation in which two players (firms) reach a state of Nash equilibrium where both firms charge a price equal to marginal cost ("MC").
The paradox is that in models such as Cournot competition, an increase in the number of firms is associated with a convergence of prices to marginal costs.
In these alternative models of oligopoly, a small number of firms earn positive profits by charging prices above cost.
On the other hand, if either firm were to lower its price, even a little, it would gain the whole market and substantially larger profits.
[4] 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); firms have limitations on their capacity to manufacture and distribute, and two firms rarely have identical costs.