Stackelberg Competition - Credible and Non-credible Threats By The Follower

Credible and Non-credible Threats By The Follower

If, after the leader had selected its equilibrium quantity, the follower deviated from the equilibrium and chose some non-optimal quantity it would not only hurt itself, but it could also hurt the leader. If the follower chose a much larger quantity than its best response, the market price would lower and the leader's profits would be stung, perhaps below Cournot level profits. In this case, the follower could announce to the leader before the game starts that unless the leader chooses a Cournot equilibrium quantity, the follower will choose a deviant quantity that will hit the leader's profits. After all, the quantity chosen by the leader in equilibrium is only optimal if the follower also plays in equilibrium. The leader is, however, in no danger. Once the leader has chosen its equilibrium quantity, it would be irrational for the follower to deviate because it too would be hurt. Once the leader has chosen, the follower is better off by playing on the equilibrium path. Hence, such a threat by the follower would not be credible.

However, in an (indefinitely) repeated Stackelberg game, the follower might adopt a punishment strategy where it threatens to punish the leader in the next period unless it chooses a non-optimal strategy in the current period. This threat is credible because it would be rational for the follower to punish in the next period so that the leader chooses Cournot quantities thereafter.