PSU Nash Equilibrium Through Rationalizability Game Theory Question

 

 

9. Nash equilibrium through rationalizability can achieved in games with upward-sloping

best-response curves if the rounds of eliminating never-best-response strategies begin

with the smallest possible values. Consider the two-player Cournot game considered in

class in which both firms have the same constant marginal cost c and face a linear

demand curve P(Q) = α – Q. Use the best-response rules in this case (bi(qj) = 0.5(α – qj –

c)) to begin rationalizing the Nash equilibrium in that game. Start with the lowest

possible quantities for the two firms and describe (at least) two rounds of narrowing the

set of rationalizable quantities toward the Nash equilibrium.