Economic Analysis
An extensive-form representation is often used to analyze the Stackelberg leader-follower model. Also referred to as a “decision tree”, the model shows the combination of outputs and payoffs both firms have in the Stackelberg game
The image on the left depicts in extensive form a Stackelberg game. The payoffs are shown on the right. This example is fairly simple. There is a basic cost structure involving only marginal cost (there is no fixed cost). The demand function is linear and price elasticity of demand is 1. However, it illustrates the leader's advantage.
The follower wants to choose to maximise its payoff . Taking the first order derivative and equating it to zero (for maximisation) yields as the maximum value of .
The leader wants to choose to maximise its payoff . However, in equilibrium, it knows the follower will choose as above. So in fact the leader wants to maximise its payoff (by substituting for the follower's best response function). By differentiation, the maximum payoff is given by . Feeding this into the follower's best response function yields . Suppose marginal costs were equal for the firms (so the leader has no market advantage other than first move) and in particular . The leader would produce 2000 and the follower would produce 1000. This would give the leader a profit (payoff) of two million and the follower a profit of one million. Simply by moving first, the leader has accrued twice the profit of the follower. However, Cournot profits here are 1.78 million apiece (strictly, apiece), so the leader has not gained much, but the follower has lost. However, this is example-specific. There may be cases where a Stackelberg leader has huge gains beyond Cournot profit that approach monopoly profits (for example, if the leader also had a large cost structure advantage, perhaps due to a better production function). There may also be cases where the follower actually enjoys higher profits than the leader, but only because it, say, has much lower costs.
Read more about this topic: Stackelberg Competition
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