Solution
Bertrand Competition
Show the problem again
Two firms with identical marginal cost c simultaneously set prices for an identical good; all consumers buy from the cheaper firm (splitting evenly on ties). At what price does each firm sell in the Nash equilibrium?
Worked solution
Both firms price at marginal cost c, earning zero profit. Any price above c can be profitably undercut by an epsilon, capturing the whole market; pricing below c loses money. The only mutual best response is p₁ = p₂ = c. The striking implication (the Bertrand paradox) is that just two price-setting competitors suffice to reach the perfectly competitive outcome.
Source: Joseph Bertrand's (1883) critique of the Cournot model. Statement written for AxiomIQ.