In microeconomics, the Bertrand–Edgeworth model of price-setting oligopoly looks at what happens when there is a homogeneous product (i.e. consumers want to buy from the cheapest seller) where there is a limit to the output of firms which are willing and able to sell at a particular price.
The argument is simple: if one firm sets a price above marginal cost then another firm can undercut it by a small amount (often called epsilon undercutting, where epsilon represents an arbitrarily small amount) thus the equilibrium is zero (this is sometimes called the Bertrand paradox).
The Bertrand approach assumes that firms are willing and able to supply all demand: there is no limit to the amount that they can produce or sell.
Huw Dixon showed that in general a mixed strategy Nash equilibrium will exist when there are convex costs.
There have been several responses to the non-existence of pure-strategy equilibrium identified by Francis Ysidro Edgeworth and Martin Shubik.