General Oligopolies - Nonlinear Oligopolies: Stability and Bifurcations - page 126

1

R 1

x 2

E S

R 2

x 1

0 1

(a)

1

x 2

E S

E 2

R 2

E 1

R 1

0 x 1 1

(b)

Fig. 3.10 Oligopolies with linear inverse demand function and cost externalities. The case of
duopoly, multiple Nash equilibria become a possibility. ( a ) A unique interior Nash equilibrium
occurs when 1 D 3, 2 D 3:5.( b ) Three interior Nash equilibria occur when 1 D 3:7, 2 D 3:5

In order to keep the following analysis tractable, we make the (rather reasonable)
assumption that the influence of each firm's action on the marginal costs of the
competitor is identical for both firms, that is

1 D 2 D : (3.20)