12-Dynamic Games

12-Dynamic Games - Dynamic Games and First and Second...

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Dynamic Games and First and Second Movers 1

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In a wide variety of markets firms compete sequentially one firm makes a move new product advertising second firms sees this move and responds These are dynamic games may create a first-mover advantage or may give a second-mover advantage may also allow early mover to preempt the market Can generate very different equilibria from simultaneous move games 2 Introduction
Interpret first in terms of Cournot Firms choose outputs sequentially leader sets output first, and visibly follower then sets output The firm moving first has a leadership 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 3 Stackelberg

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Assume that there are two firms with identical products As in our earlier Cournot example, let demand be: P = A – B.Q = A – B(q 1 + q 2 ) Marginal cost for for each firm is c 4 Stackelberg equilibrium Firm 1 is the market leader and chooses q 1 In doing so it can anticipate firm 2’s actions So consider firm 2. Residual demand for firm 2 is: P = (A – Bq 1 ) – Bq 2 Marginal revenue therefore is: MR 2 = (A - Bq 1 ) – 2Bq 2
5 Stackelberg equilibrium MR 2 = (A - Bq 1 ) – 2Bq 2 MC = c Equate marginal revenue with marginal cost q* 2 = (A - c)/2B - q 1 /2 q 2 q 1 R 2 (A – c)/2B (A – c)/B This is firm 2’s best response function Firm 1 knows that this is how firm 2 will react to firm 1’s output choice Firm 1 knows that this is how firm 2 will react to firm 1’s output choice So firm 1 can anticipate firm 2’s reaction So firm 1 can anticipate firm 2’s reaction Demand for firm 1 is: P = (A - Bq 2 ) – Bq 1 But firm 1 knows what q 2 is going to be P = (A - Bq* 2 ) – Bq 1 P = (A - (A-c)/2) – Bq 1 /2 P = (A + c)/2 – Bq 1 /2 Marginal revenue for firm 1 is: MR 1 = (A + c)/2 - Bq 1 (A + c)/2 – Bq 1 = c Solve this equation for output q 1 q* 1 = (A – c)/2B (A – c)/2B q* 2 = (A – c)/4B (A – c)/4B S Equate marginal revenue with marginal cost From earlier example we know that this is the monopoly output.

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