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Managerial Economics & Business Strategy: Game Theory in Oligopoly

Learn about game theory and its application in managerial economics, specifically in the context of oligopoly. Understand the concepts of dominant strategies, Nash equilibrium, and coordination games. Explore real-world examples and their implications.

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Managerial Economics & Business Strategy: Game Theory in Oligopoly

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  1. Welcome to EC 209: Managerial Economics- Group ABy:Dr. Jacqueline Khorassani Week Eleven

  2. Managerial Economics- Group A Week Eleven- Class 1 Monday, November 12 11:10-12:00Fottrell (AM) Aplia assignment is due tomorrow before 5 PM

  3. I received Questions • What is the format of the exam? • If you are leaving Dec. 1 who will be grading our exams? • There are aplia assignments online through mid December, well after classes are over. How many more aplia assignments are there?Thank you.

  4. Answers • I will give you the format of the exam and who will grade it soon. • There are two more aplia assignments after this week • A total of 10 assignments • Only the top 8 count

  5. Question • in this weeks aplia assignment, Q7, we have to get the reaction function of 2 microbreweries given their demand functions.   To do this we have to find MR and set it equal to MC. I have done this and none of the answers given match the answer i got even though i have tried it many times following the matching question in the practice set. I was wondering if you could check if the right answer is included in the ones given or not.Thanks

  6. Answer • Please note that the hint in question 7 of the graded assignment due next Tuesday is incorrect. The correct hint is as follows: • When a firm's demand has the form Q1 = a - bP1 + cP2 (where a, b and c are constants), Firm 1 has marginal revenue of MR1 = a + cP2 - 2bP1 • (Note that the hint on number 7 in the practice assignment is correct)

  7. Managerial Economics & Business Strategy Chapter 10 Game Theory: Inside Oligopoly

  8. What is a game? • A situation in which players make strategic decisions. • A strategy is a plan of action for playing the game. • A payoff is the value associated with a possible outcome. • Initially, we will assume rationality on the part of players. • A key issue is what kind of information is available to the players.

  9. Non-cooperative vs. Cooperative Games • A cooperative game • participants can negotiate binding contracts that allow them to plan joint strategies • Example: bargaining over the price of a car.

  10. Non-cooperative vs. Cooperative Games • Non-Cooperative Games • Both players have to make decisions without knowing what the other player is going to do. • Example: Prisoner’s Dilemma game.

  11. What are Normal Form Games? • Simultaneous-move games versus sequential move games • One-shot game versus repeated games • A Normal Form Game consists of: • Players. • Strategies or feasible actions. • Payoffs.

  12. What is a dominant strategy? • A player has a dominant strategy if it would choose a particular strategy regardless of what the other player does.

  13. Example 1: Player A can choose Up or Down while player B can choose Left or Right.First payoff in each cell is the payoff for Player A. Who has a dominant strategy? A What should B do? Left

  14. What is Nash Equilibrium? • A set of strategies such that each player is doing the best it can given the strategy of the other players. • (Up, Left) is a Nash equilibrium

  15. 11,10 10,11 12,12 10,15 10,13 13,14 Example 2 Player 2 12,11 11,12 14,13 Player 1 Does anyone have a dominant strategy? Yes, Player 1 does

  16. 11,10 10,11 12,12 10,15 10,13 13,14 Example 2 • Regardless of whether Player 2 chooses A, B, or C, Player 1 is better off choosing “a”! • “a” is Player 1’s Dominant Strategy! Player 2 12,11 11,12 14,13 Player 1

  17. 11,10 10,11 12,12 10,15 10,13 13,14 What should player 2 do? • 2 has no dominant strategy! • But 2 should reason that 1 will play “a”. • Therefore 2 should choose “C”. Player 2 12,11 11,12 14,13 Player 1

  18. Player 2 Player 1 11,10 10,11 12,12 10,15 10,13 13,14 The Outcome 12,11 11,12 14,13 • This outcome is a Nash equilibrium: • “a” is player 1’s best response to “C”. • “C” is player 2’s best response to “a”.

  19. Example 3: Simultaneous moves. One-shot game Is Nash Equilibrium the best outcome? No, High-High is Both have incentive to cheat What would A do? Low Price What would B do? Low price Nash Equilibrium? Low Price-Low Price

  20. Managerial Economics- Group A • Week Eleven- Class 2 • Tuesday, November 13 • Cairnes • 15:10-16:00 • Aplia assignment is due before 5PM today • Question 7 is deleted • If you have submitted this assignment already you should go back to the work you submitted and delete any answers you submitted on question 7.

  21. The Market-Share Game in Normal Form Manager 2 Manager 1 Does anyone have a dominant strategy? Both do

  22. Market-Share Game Equilibrium Manager 2 Manager 1 Nash Equilibrium

  23. Example 4 – Advertising Game Does anyone have a dominant strategy? Both do What is the Nash Equilibrium? Both advertise

  24. Example 5 – Coordination game There is an incentive to cooperate Who has a dominant strategy? No one There are two Nash equilibria

  25. Example 6 – Monitoring employees What should manger do? Say she will monitor but actually not do it Incentive to hide strategy What is the equilibrium? No equilibrium Who has a dominant strategy? No one

  26. Infinitely repeated games • In many situations the players interact with each other on a regular basis. • Remember that a euro earned today is worth more than euros earned in the future. • Remember from before that If the profit is the same in each period and the horizon is infinite, then PV = π (1+i)/i • PV is Present Value • where π is the profit earned in each period, • i is the discount rate.

  27. What is the Nash Equilibrium in a one shot game? Both Firms charge low price.

  28. What if the Pricing Game is repeated & the firms agree to charge a high price ? • A trigger strategy is a strategy that is contingent on the past plays of the game. • Trigger strategy: • If one firm cheats the other will charge the lower price forever. Let’s examine the incentives to cheat under this strategy.

  29. What If Firm A cheats? What is the PV of cheating? Present value of cheating is 50 + 0 + 0 + …. = 50. Present value of cooperating is 10 + 10 /(1+i)+ 10 (1+i)2 + … = 10 (1+i)/i. Cheating is the better option if 50 > 10(1 + i)/i. This is true when i > 0.25 (25 per cent).

  30. Key Insights: • Not all games are games of conflict. • Communication can help solve coordination problems. • Sequential moves can help solve coordination problems.

  31. Factors affecting collusion in repeated games • Knowledge of other firms • Knowledge of customers of other firms • Knowledge of when collusive agreements are broken • Is punishment possible? • Are threats credible?

  32. Finitely Repeated Games: Uncertain final period • Suppose the firms do not know the exact date at which the game ends. • Suppose the probability that the game will end after a given play is Φ, where 0 < Φ < 1.

  33. Suppose Φ = 0.4, that means that probability of not ending the game is 0.6 • There is a 0.4 (40%) chance that the game will end after one play, • There is a 0.6 * 0.4 = 0 .24 (24%) chance it will end after two plays • There is a 0.6 * 0.6 * 0.4 = 0.144 (14%) chance it will end after three plays • ….Probability of ending the game zero

  34. Therefore • A finitely repeated game when there is uncertainty about the final period turns out to be exactly the same as an infinitely repeated game.

  35. Managerial Economics- Group A • Week Eleven- Class 3 • Thursday, November 15 • 15:10-16:00 • Tyndall • Next Aplia Assignment is due before 5 PM on Tuesday, November 20

  36. Exam Schedule is now available • Tuesday December 4 • 9:30 – 12:30

  37. Format of Exam • Section A (100 marks) • 20 MCQ • Select no more than one option for each question and carefully follow the instructions on the MCQ answer sheet. For each question in Section A, you will receive 5 marks for a correct answer, –1.25 marks for an incorrect answer and a mark of 0 if the question is not answered. • Section B (200 marks) • Answer 3 of the following 5 questions. • Each question is worth equal marks. • Each question has 4-5 different parts • There are no long essay questions

  38. How prepare for exam? • Study all the assigned chapters of both books • Chapters 1-11 of Baye • Chapter 8 of Frank • Paper by Jensen • Work on the end of the chapter questions. • Study notes/ my slides on my webpage and Brendan’s slides on blackboard • Review all Aplia questions. • Three sample exams are posted on blackboard. Review previous exams especially 05/06 • Attend the Review Session that has been scheduled for 7 p.m. in O'Flaherty Theatre. On Monday, November 19 • I will be here a week after the classes are finished. Ask me questions.

  39. Other issues • Only 8 of the aplia assignments will count towards the final exam. • The 35% rule applies for Commerce students. This means that commerce students must get 35% in the final exam before their assignment work can be counted. • Exams of Group A & Group B are identical • Before I leave, Brendan and I will prepare an answer key for the exam. • He will then correct all the exams according to the key.

  40. Finitely Repeated Games: Uncertain final period Suppose that the firms collude & charge high and high the trigger strategy is the same (if one firm cheats the other will charge the lower price forever) suppose the interest rate is 0 Probability of ending is Φ

  41. Let’s compare profits from cheating with profits from not cheating Set 50 = 10/Φ and solve for Φ Profits are equal if Φ= 0.2 Profits from cheating are greater than the profits of cooperating if Φ > 0.2 • Profits (Π) from cheating are 50. • Profits from not cheating are • 10 + (1- Φ).10 + (1- Φ)2.10 +…… = 10/Φ

  42. Key Insight • It is more likely to sustain the collusion if • Preset value of cheating is less than the present value of cooperating • Interest rates are low • Probability of ending is low • The ability of monitoring the action of rivals is high • Fewer firms • The ability of punishing the cheaters is high • Reputation matters

  43. A Pricing Game that is repeated: known final period • Suppose for simplicity that there are two rounds to this game. • Both players know that the game ends after the second period. • A trigger strategy will not work in this case. • Neither firm has an incentive to cooperate in the last period since there is no punishment for cheating. • Since the firms are certain to cheat in the final round there is no incentive to cooperate in the first round. • The result is that both firms always cheat. • The result is the same regardless of the number of rounds.

  44. A Pricing Game that is repeated: unknown final period • An alternative strategy is to play Tit-for-tat. This means that you cooperate on the first round and then you do whatever the other player did in the previous round. • Tit-for-tat strategy requirements • Players recall other player’s moves • Players have a stake in future outcomes

  45. Sequential (multistage) games • An extensive-form game summarizes • who the players are, • the information available to the players at each stage of the game, • the strategies available to the players, • the order of the moves and • the payoffs that result from the various strategies.

  46. Sequential (multistage) games (A has to move first) Suppose B threatens that he will choose Down no matter what What is the best strategy for A? Chose down Is (Down, Down) a Nash equilibrium? yes Is this a reasonable outcome? Should A believe B’s threat to choose Down if A chooses Up? No, this is not a reasonable outcome

  47. Sequential (multistage) games • Suppose B’s strategy is to choose up if player A chooses up and down if A chooses down. • This leads to the equilibrium (up, up). • This is also a Nash equilibrium. This equilibrium is a sub-game perfect equilibrium – at each stage of the game neither player can improve its payoffs by changing its strategy. This is a more reasonable Equilibrium because it doesn’t involve threats that are not credible.

  48. The Pricing to Prevent Entry Game in Extensive Form • Suppose B is an existing firm in the market and A is a potential entrant. • B can react to A’s entry by either lowering price or leaving price unchanged.

  49. The Pricing to Prevent Entry Game in Extensive Form -1, 1 Lower price Incumbent (B) Leave price unchanged Enter 5, 5 Entrant (A) Stay Out 0, 10 B is threatening to lower its price if A enters, is this a credible threat? No

  50. Is there a Nash Equilibrium (NE)? -1, 1 There are 2 NEs Lower price Incumbent (B) Leave price unchanged Enter Entrant (A) 5, 5 Stay Out 0, 10 Another NE: if A enters and B leaves price unchanged This is sub game prefect NE Yes, if B threatens to lower the price if A enters NE is for A to stay out

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