Collusion between cournot duopolists:

Friedman was first to show that cooperation could be achieved in an infinitely repeated game by  using trigger strategies that switch forever  to  the stage game Nash equilibrium following any deviation. The original application was to collusion in a Cournot oligopoly.

If the aggregate quantity  in  the market is Q =  (q₁ +  q₂), and the market clearing price  is P = a - Q. Assuming Q <  a, and  each  firm has  a marginal cost  c,  if  the firms' choose  their quantities simultaneously,  then  the  unique Nash  equilibrium  of  the  game  is both firm producing (a  -  c)/3, which  we  call  the Cournot  quantity and  denote  it  by  q_c.

Since the  equilibrium aggregate quantity  2(a  -  c)/3, exceeds  the  monopoly.  Clearly, both the firms would  be  better off  if each firm  quantity q_m  = (a  -  c)/2 .produced half of q_m,  the monopoly quantity (a  -  c)/4.

We  will  consider  an  infinitely  repeated  game  based  on  this Cournot stage game when both  the firms have the discount factor δ. We will seek  for a sub- game  perfect  Nash  equilibrium  in  which  both  the  firms collude  and  their payoffs are more than Cournot payoff.