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

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Dynamic Games and First and Second Movers 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
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
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 4
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.
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern