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Topic 8: Oligopoly and game theory

A ntitrust Economics 2013. David S. Evans University of Chicago, Global Economics Group. Elisa Mariscal CIDE, ITAM, CPI. Topic 8: Oligopoly and game theory. Topic 8 | Part 2 6 June 2013. Date. Overview: . Oligopoly and Interdependent Behavior. Oligopoly and interdependent b ehavior.

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Topic 8: Oligopoly and game theory

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  1. Antitrust Economics 2013 David S. Evans University of Chicago, Global Economics Group Elisa Mariscal CIDE, ITAM, CPI Topic 8: Oligopoly and game theory Topic 8 | Part 2 6 June 2013 Date

  2. Overview:

  3. Oligopoly and Interdependent Behavior

  4. Oligopoly and interdependent behavior

  5. The Role of strategic behavior: key features

  6. Oligopoly models and their different assumptions

  7. Price PA D(P) D(PA ) Basic Cournot model for two-firms: assumptions A possible price that firm A might consider The market demand schedule Marginal revenue MC Q The quantity firm A would sell if firm B supplied nothing.

  8. Price D(P) Firm A’s decision based on its conjecture about how much firm B will offer Market demand MC Q Residual demand for Firm A if Firm B sells q1B q1B

  9. Price D(P) Firm A’s profit-maximizing output given firm B’s output decision Price Residual demand for Firm A when Firm B produces q1B MC MC q1A Q q1B MR for Firm A given its residual demand

  10. Price Firm A’s decision on how much to supply varies with its conjecture about firm B’ssupply D(P) Residual demand for Firm A when Firm B produces q1B MC q1A Q q1B MR for Firm A given its residual demand

  11. The “best response curve” summarizes A’s best moves for each of B’s choices

  12. The reaction function is linear when demand Is linear qA Firm A produces the monopoly level when firm B produces nothing Firm A’s Reaction Function qMA q1A Firm A supplies nothing to the market if Firm B supplies the entire market(by pricing at marginal cost—i.e., the competitive level) since it can’t make any profit. q2A q1B q2B qB qC

  13. Firm B also has a reaction function based on a similar analysis qA q C Firm B’s Reaction Function q M Firm A’s Reaction Function qB q M q C Note Firm A and Firm B’s reaction functions are being drawn from different orientations (i.e. B on the horizontal axis is looking at what A on the vertical axis is doing; while A on the vertical axis is looking at what B on the horizontal axis is doing.

  14. qA Firm B’s Reaction Function Equilibrium qMA Firm A’s Reaction Function qMB qCOURNOTB qCB The Cournot equilibrium occurs where the reaction functionscross Verify for the Cournot output it is less than the competitive level but greater than the monopoly level. qCA qCOURNOTA Total output = 2 x qCOURNOTA,B=qCOURNOTA+qCOURNOT B

  15. With Cournot oligopoly, total price is more than with competition but less than with monopoly P D(P) MONOPOLY PM COURNOT PCOURNOT COMPETITION MC Q qMA,B Q COURNOT qC

  16. Introduction to the Bertrand model

  17. PB PA D(P) QA =D(PA < PB) Q Firm A’s decision based on its conjecture about firm B’s price Firm B charges a higher price but gets zero demand P

  18. The Best Strategy with Bertrand Competition

  19. Equilibrium with Bertrand competition

  20. Bertrand model with product differentiation

  21. Cournot and Bertrand can both be restated as games

  22. Oligopoly theory and the embarrassment of riches

  23. Dynamic Games of Competition

  24. Dynamic Games Entrant gets 4, Incumbent 5 Incumbent Entrant

  25. Dynamic Equilibria and Credible Threats for the Entry Game

  26. Entrant Stay out Enter Incumbent 0 10 Fight Accommodate -1 0 4 5 Dynamic Games and Game Trees

  27. Solving the Game: Backward Induction

  28. Entrant Stay out Enter Incumbent 0 10 Fight Accommodate -1 0 4 5 Nash Equilibrium for the Entry Game

  29. Making Credible Commitments

  30. Next week: Makeup Lecture 6.2

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