Solution to Exercise

The best response function of firm 1 is b1(y2) = (90  y2)/2 (see example) and the best response function of firm 2 is b2(y1) = (120  y1)/4 (see example).

Thus the Nash equilibria are the solutions of the equations

y1 = (90  y2)/2
y2 = (120  y1)/4.
These equilibria have a single solution, (y1y2) = (240/7, 150/7). Thus the game has a unique Nash equilibrium, (y1y2) = (240/7, 150/7).