Modified and Extended Oligopolies - Nonlinear Oligopolies: Stability and Bifurcations - page 149

1 − a 1 (1 + r 1 ) 1 − a 2 (1 + r 2 ) 1 − a S -2 (1 + r S -2 ) 1 − a S -1 (1 + r S -1 ) 1 − a S (1 + r S )

λ

Fig. 4.3 The discrete time model of labor-managed oligopolies. The determination of the
eigenvalues that are roots of the graph of g./, plotted here for j >0for all j

1− a 1 (1+ r 1 ) 1− a 2 (1+ r 2 ) 1 − a S -1 (1 + r S -1 ) 1− a S (1+ r S )

λ

Fig. 4.4 The discrete time model of labor-managed oligopolies. The determination of the
eigenvalues that are roots of the graph of g./, plotted here for j <0for all j

has to be constant. This property also follows directly from the special form of the
payoff function

x k .A Bx k BQ k / d k
p k x k

' k .x 1 ;:::;x N / D W (4.13)

A Bx k BQ k
p k

W ;

d k
p k x k C

D (4.14)