1.5.       Consider the following two finite versions of the Cournot duopoly model. First, suppose each  firm  must  choose  either half  the monopoly quantity, qm/ 2 = (a - c)/4, or the Cournot equilib­ rium quantity, qc = (a - c)/3. No other  quantities  are  feasible. Show that this two-action game is equivalent to the Prisoners' Dilemma: each firm has  a  strictly  dominated  strategy,  and  both are worse off in equilibrium than they  would  be  if  they  cooper­ ated. Second, suppose each  firm  can choose  either  qm / 2, or qc,  or a third quantity, q'. Find a value for q' such that the game is equivalent to the Cournot model in Section 1.2.A, in the sense that (qc, qc) is a unique Nash equilibrium  and both  firms are worse off  in equilibrium than they could be if  they  cooperated, but  neither firm  has  a  strictly  dominated strategy.