Stackel Berg Model in Oligopoly

StackelBerg’s Model and Collusion

This note explores the economics of first‐mover advantages and collusion in oligopolyMarkets. Last chapter we examined two basic strategies in oligopoly markets: price competition and strategic capacity decisions. We emphasized that when setting your firm’s strategy, it becomes important to consider your competitors actions (or reactions). Your profit maximizing strategy may depend, perhaps quite delicately, on what you expect your rivals to do and conversely.

This chapter examines two more sophisticated ways that firms may interact in oligopoly markets. In our analysis of market outcomes when firms make strategic capacity decisions that is, Cournot’s solution—there is an important feature that deserves more attention.

This is the matter of timing and commitment. We’ll first explore what happens if one firm has the advantage of setting its strategy before its rivals are able to. We call this a first‐mover advantage, and we’ll see that it can increase profits further yet.

Second, we’ll then look at another market outcome that students and business managers often come up with and think about: collusion. This can raise firms’ profits even further,but it is both rarely successful and it is prohibited by law (in the U.S. and E.U.) To understand why, we’ll need to do a bit of economics.

First‐Mover Advantages

To begin, let’s consider the same market we examined in the last chapter.

To recap: We have two firms (a duopoly) that produce the same product. The two firms have different cost structures, however. The total costs for firm 1 and firm 2 are, respectively,

TC1 = 5 * q1 and TC2 = 0.5 * (q2)2

where q1 is the output of firm 1, and q2 is the output of firm 2. These imply that firm 1’s cost structure provides significant economies at high volume, while firm 2’s costs are initially lower but then rise quickly. Market demand for this product depends upon industry wide production according to the demand function

P = 100...