Question

Two firms A and B engage in price competition, in a market where all consumers have reservation prices of 20 dollars. Firm A has unit costs of cA = 10, and firm B unit costs of cB = 15. Find (explain the strategies!) the ’most plausible’ Nash equilibrium in the Bertrand game where both firms simultaneously post their prices (pA, pB). Then, briefly characterize other equilibria in this game. In which sense are these latter equilibria ’less plausible’?

Answer 1

In case of Bertrand competition, The Nash equilibrium occurs at the point where price that firms charge is equal to marginal cost of production of firms. In case of different marginal cost of production of firms, the lower of the marginal cost of production is the Nash equilibrium of the game. Thus, the most plausible Nash equilibrium in the Bertrand game where both firms simultaneously post their prices is Pa = Pb = $10.

The other equilibria of the game is prices above the marginal cost of production of firms when both enter into collusive agreement to charge a higher price to make profits. But firms in this case, have an incentive to reduce prices and increase the quantity sold and increase more revenue as compared to another firm by attracting more consumers by charging lower prices and thus increasing profits,. But in another period another firm will also charge a lower price and thus both will reduce their prices equal to their marginal cost of production. Thus, the latter equilibria is less plausible.