We consider a homogeneous goods industry in which firms compete in quantities (Cournot competition). Let  = {0, 1, 2, … , N } denote the (initial) set of firms. All firms have constant returns to scale; firm i’s marginal cost is denoted  ci  . Inverse
demand is given by P(Q ). We impose standard assumptions on demand:

ASSUMpTION 1: For all Q such that P(Q ) > 0, we have:
(i )  P′ (Q ) + q P″ (Q ) < 0 for all q ∈ [ 0, Q ];
(ii ) li m Q→∞  P(Q ) = 0.
Under these conditions there exists a unique Nash equilibrium in quantities .



为什么these assumptions ensure the existence of a unique stable NE in cournot competition？