Based on: Tadelis, S. (2013). Game theory : an introduction. Princeton University Press.

Consider the Bertrand game with c1(q1) = 100q1 and c2(q2) = 120q2, demand equal to p = 10000 q, and where firms must choose prices in increments of twenty HUF. The whole demand goes to the firm which offers lower prices and if both firms have the same price, the market is shared equally.

a) How many Nash equilibria in pure strategies does the game have? Describe them.

b) What happens to the set of equilibria in pure strategies if a third firm enters the market with c3(q3) = 100q3?