Bertrand Model

Model
Two firms with the same marginal cost (MC=c), producing a homogeneous product and competing in prices.

homogeneous product → consumers purchase from cheapest firms

Bertrand's theorem
Let (p1*,p2*) be a Nash Equilibrium. Then, p1*=p2*=c.

If each firm has a different marginal cost c1, c2 (c1<c2), the Nash equilibria are (p1, p2) such that c1≤p1=p2≤c2.

http://en.wikipedia.org/wiki/Bertrand_competition