Deep Thought

1. Deep Thought A verbal contract isn’t worth the paper it’s written on. ~ Yogi Berra (Translation: Today’s lesson teaches how talk is cheap.) BA 445 Lesson C.2 Cheap Talk when Interests Align

2. Readings • Readings • Baye “Coordination Game” (see the index) • Dixit Chapter 9 BA 445 Lesson C.2 Cheap Talk when Interests Align

3. Overview • Overview BA 445 Lesson C.2 Cheap Talk when Interests Align

4. Overview Lesson 2 considers games where players easily reveal information about their own moves when players’ interests align. BA 445 Lesson C.2 Cheap Talk when Interests Align

5. Overview BA 445 Lesson C.2 Cheap Talk when Interests Align

6. Example 1: Cheap Talk given Minor Conflict Example 1: Cheap Talk given Minor Conflict BA 445 Lesson C.2 Cheap Talk when Interests Align

7. Example 1: Cheap Talk given Minor Conflict Overview Cheap Talk given Minor Conflict is a good way to make your actions predictable to your allies (whose interests align). It can change outcomes by changing players’ beliefs about other players’ actions. BA 445 Lesson C.2 Cheap Talk when Interests Align

8. Example 1: Cheap Talk given Minor Conflict Comment: The simplest way to give information to others seems to be to tell them, and the simplest way to get information is to ask. But in a game of strategy, players are aware that others may not tell the truth, and there own talk may not be believed by others. It is said that talk is cheap; that is, talk has zero or negligible direct cost. However, it can indirectly affect the outcome and payoffs of a game by changing one player’s beliefs about another player’s actions, and so selecting one equilibrium out of multiple equilibria. BA 445 Lesson C.2 Cheap Talk when Interests Align

9. Example 1: Cheap Talk given Minor Conflict Call talk that has no direct cost cheap talk. For a game with cheap talk, call an equilibrium that is affected by talk a cheap-talk equilibrium. The central question is whether it is possible that the speaker tells the truth, or whether he must be lying. So for each cheap-talk game, ask: Is there a cheap-talk equilibrium with truthful communication? BA 445 Lesson C.2 Cheap Talk when Interests Align

10. Example 1: Cheap Talk given Minor Conflict Question: Consider the Format Game between The Blu-ray Disc Association and Toshiba. Suppose that at the same time each player either adopts the Blu-ray format or the HD format. Suppose if both adopt the same format, then both gain $100 million from customers that value the convenience of having a universal format. Suppose if they both adopt the Blu-ray format, then The Blu-ray Disc Association gains an extra $10 million since their expertise with that format gives them lower production costs. Suppose if they both adopt the HD format, then Toshiba gains an extra $10 million since their expertise with that format gives them lower production costs. Finally, suppose that, before the game is played, The Blu-ray Disc Association is given an opportunity to communicate either “I will choose Blu-ray” or “I will choose HD”. Is there a cheap-talk equilibrium with truthful communication? If so, find it. BA 445 Lesson C.2 Cheap Talk when Interests Align

11. Example 1: Cheap Talk given Minor Conflict Answer: First, complete the normal form below for the Format Game. For example, if The Blu-ray Disc Association and Toshiba both adopt HD, then both gain $100 million from customers that value the convenience of having a universal format, and Toshiba gains an extra $10 million since their expertise with the HD format gives them lower production costs. BA 445 Lesson C.2 Cheap Talk when Interests Align

12. Example 1: Cheap Talk given Minor Conflict Define a game tree of this Cheap-Talk-Format Game. Create a first stage to the game where The Blu-ray Disc Association makes one of two statements --- “I will choose Blu-ray” or “I will choose HD”. The second stage is Toshiba’s choice of format --- assuming Toshiba believes Blu-ray’s statement. And the third stage is The Blu-ray Disc Association’s choice of format --- after they deduced Toshiba’s choice based on Toshiba believing Blu-ray’s statement. BA 445 Lesson C.2 Cheap Talk when Interests Align

13. Example 1: Cheap Talk given Minor Conflict Game Tree: BA 445 Lesson C.2 Cheap Talk when Interests Align

14. Example 1: Cheap Talk given Minor Conflict Modified Rollback Solution: First, Toshiba’s choice of format --- assuming Toshiba believes Blu-ray’s statement. BA 445 Lesson C.2 Cheap Talk when Interests Align

15. Example 1: Cheap Talk given Minor Conflict Modified Rollback Solution: Second, Association’s choice of format --- after they deduced Toshiba’s choice. BA 445 Lesson C.2 Cheap Talk when Interests Align

16. Example 1: Cheap Talk given Minor Conflict Modified Rollback Solution: Finally, Association’s choice of statement. Was communication truthful? Yes. BA 445 Lesson C.2 Cheap Talk when Interests Align

17. Example 2: Cheap Talk given Major Conflict Example 2: Cheap Talk given Major Conflict BA 445 Lesson C.2 Cheap Talk when Interests Align

18. Example 2: Cheap Talk given Major Conflict Overview Cheap Talk given Major Conflict is disregarded by opponents (whose interests conflict) since, if they believed you, you could exploit that belief. — So, an employer should disregard a shirker’s self assessment. BA 445 Lesson C.2 Cheap Talk when Interests Align

19. Example 2: Cheap Talk given Major Conflict Question: Consider the Work-Shirk Game for an employee and an employer. Suppose that at the same time the employee chooses to either work or shirk (not work) and the employer chooses to either monitor the employee or not monitor the employee. Suppose if the employee chooses to work, he looses $100 of happiness from the effort of working, but he yields $400 to his employer. Suppose the employer can monitor the employee at a cost of $80. Suppose if the employee chooses to not work and the employer chooses to monitor, then the employee is not paid, but in every other case (“work” or “not monitor”), then the employee is paid $150. Finally, suppose that, before the game is played, the employer is given an opportunity to communicate either “I will monitor” or “I will not monitor”. Is there a cheap-talk equilibrium with truthful communication? If so, find it. BA 445 Lesson C.2 Cheap Talk when Interests Align

20. Example 2: Cheap Talk given Major Conflict Answer: First, complete the normal form below for the Work-Shirk Game. For example, if the employee chooses to work and the employer chooses to monitor, then the employee looses $100 of happiness from the effort of working but is paid $150, and the employer gain $400 from his employer but pays $80 for monitoring and pays $150 to his employee. BA 445 Lesson C.2 Cheap Talk when Interests Align

21. Example 2: Cheap Talk given Major Conflict Define a game tree of this Cheap-Talk-Work-Shirk Game. Create a first stage to the game where the employer makes one of two statements --- “I will monitor” or “I will not monitor”. The second stage is the employee’s choice of work --- assuming the employee believes the employer’s statement. And the third stage is the employer’s choice of monitoring --- after they deduced the employee’s choice based on the employee believing the employer’s statement. BA 445 Lesson C.2 Cheap Talk when Interests Align

22. Example 2: Cheap Talk given Major Conflict Game Tree: BA 445 Lesson C.2 Cheap Talk when Interests Align

23. Example 2: Cheap Talk given Major Conflict Modified Rollback Solution: First, Employee’s choice of work -- assuming Employee believes Employer’s statement. BA 445 Lesson C.2 Cheap Talk when Interests Align

24. Example 2: Cheap Talk given Major Conflict Modified Rollback Solution: Second, Employer’s choice of monitor --- after they deduced Employee’s choice. BA 445 Lesson C.2 Cheap Talk when Interests Align

25. Example 2: Cheap Talk given Major Conflict Modified Rollback Solution: Finally, Employer’s choice of statement. Was communication truthful? No. So ignore the original message. BA 445 Lesson C.2 Cheap Talk when Interests Align

26. Example 2: Cheap Talk given Major Conflict Comment: Since there is no cheap-talk equilibrium with truthful communication, the original message should be ignored, and the game reduces to the original work-shirk game. The Nash equilibrium strategy for the Employee is the mixed strategy for which the Employer would not benefit if he could predict the Employee’s mixed strategy. Suppose the Employer predicts p and (1-p) are the probabilities the Employee chooses Work or Shirk. The Employer expects 170p - 80(1-p) from playing Monitor, and 250p - 150(1-p) from Trust. The Employer does not benefit if those payoffs equal, 170p - 80(1-p) = 250p - 150(1-p), or -80 + 250p = -150 + 400p, or p = 70/150 = 0.467 BA 445 Lesson C.2 Cheap Talk when Interests Align

27. Example 2: Cheap Talk given Major Conflict The Nash equilibrium strategy for the Employer is the mixed strategy for which the Employee would not benefit if he could predict the Employer’s mixed strategy. Suppose the Employee predicts q and (1-q) are the probabilities the Employer chooses Monitor or Trust. The Employee expects 50q + 50(1-q) from playing Work, and 0q + 150(1-q) from Shirk. The Employee does not benefit if those payoffs equal, 50q + 50(1-q) = 0q + 150(1-q), or 50 = 150 – 150q, or q = 100/150 = 0.667 BA 445 Lesson C.2 Cheap Talk when Interests Align

28. Example 3: Cheap Talk given Perfect Conflict Example 3: Cheap Talk given Perfect Conflict BA 445 Lesson C.2 Cheap Talk when Interests Align

29. Example 3: Cheap Talk given Perfect Conflict Overview Cheap Talk given Perfect Conflict is disregarded by opponents since, if they believed you, you could exploit that belief. — So, a goalie should disregard a kicker saying “I’ll kick left”. BA 445 Lesson C.2 Cheap Talk when Interests Align

30. Example 3: Cheap Talk given Perfect Conflict Question: Consider a penalty kick in soccer. The goalie either jumps left or right at the same time that the kicker either kicks left or right. The kicker’s payoffs are the probability of him scoring, and the goalie’s payoffs are the probability of the kicker not scoring. Those actions and payoffs define a normal form for this Penalty Kick Game. Finally, suppose that, before the game is played, the kicker is given an opportunity to communicate either “I will kick left” or “I will kick right”. Is there a cheap-talk equilibrium with truthful communication? If so, find it. BA 445 Lesson C.2 Cheap Talk when Interests Align

31. Example 3: Cheap Talk given Perfect Conflict Answer: Define a game tree of this Cheap-Talk-Penalty-Kick Game. Create a first stage to the game where the kicker makes one of two statements --- “I will kick left” or “I will kick right”. The second stage is the goalie’s choice of jumping left or right --- assuming the goalie believes the kicker’s statement. And the third stage is the kicker’s choice of kicking left or right --- after he deduced the goalie’s choice based on the goalie believing the kicker’s statement. BA 445 Lesson C.2 Cheap Talk when Interests Align

32. Example 3: Cheap Talk given Perfect Conflict Game Tree: BA 445 Lesson C.2 Cheap Talk when Interests Align

33. Example 3: Cheap Talk given Perfect Conflict Modified Rollback Solution: First, Goalie’s choice --- assuming Goalie believes Kicker’s statement. Goalie eliminates the choices in black. BA 445 Lesson C.2 Cheap Talk when Interests Align

34. Example 3: Cheap Talk given Perfect Conflict Modified Rollback Solution: Second, Kicker’s choice --- after he deduced Goalie’s choice. Kicker eliminates the choices in black. BA 445 Lesson C.2 Cheap Talk when Interests Align

35. Example 3: Cheap Talk given Perfect Conflict Finally, Kicker’s choice of statement. Kicker says “I will kick Right” but he actually kicks Left. Was communication truthful? No. So ignore the original message. BA 445 Lesson C.2 Cheap Talk when Interests Align

36. Example 3: Cheap Talk given Perfect Conflict Comment: Since there is no cheap-talk equilibrium with truthful communication, the original message should be ignored, and the game reduces to the original penalty-kick game. The Nash equilibrium strategy for the Kicker is the mixed strategy for which the Goalie would not benefit if he could predict the Kicker’s mixed strategy. Suppose the Goalie predicts p and (1-p) are the probabilities the Kicker chooses Left or Right. The Goalie expects .9p + .6(1-p) from playing Left, and .2p + .7(1-p) from Right. The Goalie does not benefit if those payoffs equal, .9p + .6(1-p) = .2p + .7(1-p), or .6 + .3p = .7 - .5p, or p = 1/8 = 0.125 BA 445 Lesson C.2 Cheap Talk when Interests Align

37. Example 3: Cheap Talk given Perfect Conflict The Nash equilibrium strategy for the Goalie is the mixed strategy for which the Kicker would not benefit if he could predict the Goalie’s mixed strategy. Suppose the Kicker predicts q and (1-q) are the probabilities the Goalie chooses Left or Right. The Kicker expects .1q + .8(1-q) from playing Left, and .4q + .3(1-q) from Right. The Kicker does not benefit if those payoffs equal, .1q + .8(1-q) = .4q + .3(1-q), or .8 - .7q = .3 + .1q, or q = 5/8 = 0.625 BA 445 Lesson C.2 Cheap Talk when Interests Align

38. Review Questions • Review Questions • You should try to answer some of the review questions (see the online syllabus) before the next class. • You will not turn in your answers, but students may request to discuss their answers to begin the next class. • Your upcoming cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams. BA 445 Lesson C.2 Cheap Talk when Interests Align

39. BA 445 Managerial Economics End of Lesson C.2 BA 445 Lesson C.2 Cheap Talk when Interests Align