Dynamic games and First and Second Movers (The Stackelberg Model) ECON 4100: Industrial Organization Lecture 11 Dynamic games and First and Second Movers (The Stackelberg Model)

Oligopoly Models There are three dominant oligopoly models Cournot Bertrand Stackelberg Now we will consider the Stackelberg Model (due to Heinrich von Stackelberg, 1934, about a century after Cournot’s)

Stackelberg Interpret in terms of Cournot Firms choose outputs sequentially leader sets output first, and visibly (IBM, Boeing, the leader is some easily visible firm ) follower then sets output The firm moving first has a leadership advantage or first-mover advantage can anticipate the follower’s actions can therefore manipulate the follower For this to work the leader must be able to commit to its choice of output Strategic commitment has value

Stackelberg Equilibrium: an example Both firms have constant marginal costs of $10, i.e., c = 10 for both firms Assume that there are two firms with identical products As in our earlier Cournot example, let demand be: P = 100 - 2Q = 100 - 2(q1 + q2) Total cost for for each firm is: C(q1) = 10q1; C(q2) = 10q2 Firm 1 is the market leader and chooses q1 In doing so it can anticipate firm 2’s actions So consider firm 2. Demand is: P = (100 - 2q1) - 2q2 Marginal revenue therefore is: MR2 = (100 - 2q1) - 4q2

Stackelberg equilibrium (cont.) Equate marginal revenue with marginal cost This is firm 2’s best response function Stackelberg equilibrium (cont.) Solve this equation for output q2 But firm 1 knows what q2 is going to be MR2 = (100 - 2q1) - 4q2 q2 Firm 1 knows that this is how firm 2 will react to firm 1’s output choice MR = (100 - 2q1) - 4q2 = 10 = c We can calculate that 22.5 is actually the monopoly output. This is an important result. The Stackelberg leader chooses the same output as a monopolist would. But firm 2 is not excluded from the market q*2 = 22.5 - q1/2 So firm 1 can anticipate firm 2’s reaction Demand for firm 1 is: P = (100 - 2q2) - 2q1 22.5 P = (100 - 2q*2) - 2q1 Equate marginal revenue with marginal cost P = (100 - (45 - q1)) - 2q1 S 11.25 => P = 55 - q1 Solve this equation for output q1 R2 Marginal revenue for firm 1 is: q1 MR1 = 55 - 2q1 22.5 45 55 - 2q1 = 10 => q*1 = 22.5 => q*2 = 11.25

Stackelberg equilibrium (cont.) Leadership benefits the leader firm 1 but harms the follower firm 2 Aggregate output is 33.75 Leadership benefits consumers but reduces aggregate profits q2 Firm 1’s best response function is “like” firm 2’s So the equilibrium price is $32.50 45 Firm 1’s profit is (32.50 - 10)22.5 R1 Compare this with the Cournot equilibrium  p1 = $506.25 Firm 2’s profit is (32.50 - 10)11.25  p2 = $253.125 22.5 We can check that the Cournot equilibrium is: C 15 S 11.25 qC1 = qC2 = 15 R2 q1 The Cournot price is $40 15 22.5 45 Profit to each firm is $450

Stackelberg and Commitment It is crucial that the leader can commit to its output choice without such commitment firm 2 should ignore any stated intent by firm 1 to produce 45 units the only equilibrium would be the Cournot equilibrium In fact the model is incomplete unless we manage to explain this ability to make a credible commitment It is not easy to commit in a credible manner to producing output

Stackelberg and Commitment So how to commit? prior reputation investment in additional capacity place the stated output on the market Therefore, commitment could be better understood in terms of committing to the capability of producing output We want to locked-in the cost of capacity (a sunk cost) to show that we mean business. This investment needs to be visible for it to be worthwhile

Stackelberg and timing Finally, the timing of decisions matters (for some reason, one firm got there first and then has a way to commit through sunk investments in capacity) There is much more we can learn later in terms of entry-deterrence too

Stackelberg and Efficiency If unit costs are constant, Stackelberg’s equilibrium will result in a Pareto improvement relative to Cournot’s equilibrium, because the quantity produced increases However, if the leader is relatively inefficient, then we cannot really say if this equilibrium will be better than the simultaneous choice of output Passing output production from the efficient follower to the inefficient leader imposes an inefficiency that might not be counteracted by the efficiency increase associated with extra overall output …and Stackelberg leaders can get very inefficient in real life (due to X-inefficiency for example)

Next: Monopoly Power and Predatory Conduct We will learn about: Entry and exit, predatory conduct, and incumbent/entrant firm models Dynamic strategic interaction and credible commitment Limit pricing and public policy