1. Chapter 5 Game Theory and the Tools of Strategic Business Analysis

2. Game Theory 0 Game theory applied to economics by John Von Neuman and Oskar Morgenstern 0 Game theory allows us to analyze different social and economic situations

3. Games of Strategy Defined 0 Interaction between agents can be represented by a game, when the rewards to each depends on his actions as well as those of the other player 0 A game is comprised of 0 Number of players 0 Order of play 0 strategies 0 Chance 0 Information 0 Payoffs 3

4. Example 1:Prisoners’ Dilemma 0 Two people committed a crime and are being interrogated separately. 0 The are offered the following terms: 0 If both confessed, each spends 8 years in jail. 0 If both remained silent, each spends 1 year in jail. 0 If only one confessed, he will be set free while the other spends 20 years in jail.

5. Example 1: Prisoners’ Dilemma 5 Prisoner 2 confesssilent Prisoner 1 Confess8, 80, 20 Silent20, 01, 1 0 Numbers represent years in jail 0 Each has a dominant strategy to confess 0 Silent is a dominated strategy 0 Nash equilibrium: Confess Confess

6. Example 2: Matching Pennies 6 Player 2 HeadsTails Player 1 Heads- 1, +1+1 - 1 Tails+1 - 1- 1, +1

7. Example 3: Oligopoly Game 7 General Motors High priceLow price Ford High price500, 500100, 700 Low price700, 100300, 300 0 Similarly for GM 0 The Nash equilibrium is Price low, Price low

8. Game Types 0 Game of perfect information 0 Player – knows prior choices 0 All other players 0 Game of imperfect information 0 Player – doesn’t know prior choices 8

9. Representing Games 0 The previous examples are of 0 Simultaneous games 0 Games of imperfect information Games can be represented visually in 0 Bi- matrix form 0 Table 0 Dimensions depend on the number of strategies 0 Game tree 0 Extensive form game 9

10. Matching Pennies 10 Player 2 HeadsTails Player 1 Heads- 1, +1+1 - 1 Tails+1 - 1- 1, +1 Game of imperfect information Represented in bi-matrix form

11. Extensive form of the game of matching pennies 11 Child 2 does not know whether child 1 chose heads or tails. Therefore, child 2’s information set contains two nodes. Child 1 Child 2 Tails Heads Tails Heads Tails Heads - 1 +1 - 1 +1 - 1 +1

12. Strategy 0 A player’s strategy is a plan of action for each of the other player’s possible actions

13. Game of perfect information 13 Player 2 (Toshiba) knows whether player 1 (IBM) moved to the left or to the right. Therefore, player 2 knows at which of two nodes it is located 1 2 3 IBM Toshiba UNIX DOS UNIX DOS UNIX DOS 600 200 100 200 600 In extensive form

14. Strategies 0 IBM: 0 DOS or UNIX 0 Toshiba 0 DOS if DOS and UNIX if UNIX 0 UNIX if DOS and DOS if UNIX 0 DOS if DOS and DOS if UNIX 0 UNIX if DOS and UNIX if UNIX

15. 15 Toshiba (DOS | DOS, DOS | UNIX) (DOS | DOS, UNIX | UNIX) (UNIX | DOS, UNIX | UNIX) (UNIX | DOS, DOS | UNIX) IBM DOS600, 200 100, 100 UNIX100, 100200, 600 100, 100 Game of perfect information In normal form

16. Game of imperfect information 0 Assume instead Toshiba doesn’t know what IBM chooses 0 The two firms move at the same time 0 Imperfect information 0 Need to modify the game accordingly

17. Game of imperfect information 17 Toshiba does not know whether IBM moved to the left or to the right, i.e., whether it is located at node 2 or node 3. 1 2 3 IBM Toshiba UNIX DOS UNIX DOS UNIX DOS 600 200 100 200 600 In extensive form Information set Toshiba’s strategies: DOS UNIX

18. 18 Toshiba DOSUNIX IBM DOS600, 200100, 100 UNIX100, 100200, 600 Game of imperfect information In normal form

19. Equilibrium for Games Nash Equilibrium 0 Equilibrium 0 state/ outcome 0 Set of strategies 0 Players – don’t want to change behavior 0 Given - behavior of other players 0 Noncooperative games 0 No possibility of communication or binding commitments 19

20. Nash Equilibria 20

21. 21 Toshiba DOSUNIX IBM DOS600, 200100, 100 UNIX100, 100200, 600 Nash Equilibrium: Toshiba-IBM imperfect Info game The strategy pair DOS DOS is a Nash equilibrium. Are there any other equilibria?

22. Dominant Strategy Equilibria 0 Strategy A dominates strategy B if 0 A gives a higher payoff than B 0 No matter what opposing players do 0 Dominant strategy 0 Best for a player 0 No matter what opposing players do 0 Dominant-strategy equilibrium 0 All players - dominant strategies 22

23. Oligopoly Game 23 General Motors High priceLow price Ford High price500, 500100, 700 Low price700, 100300, 300 0 Ford has a dominant strategy to price low 0 If GM prices high, Ford is better of pricing low 0 If GM prices low, Ford is better of pricing low

24. Oligopoly Game 24 General Motors High priceLow price Ford High price500, 500100, 700 Low price700, 100300, 300 0 Similarly for GM 0 The Nash equilibrium is Price low, Price low

25. Prisoners’ Dilemma 25 Prisoner 2 confesssilent Prisoner 1 Confess8, 80, 20 Silent20, 01, 1 0 Numbers represent years in jail 0 Each has a dominant strategy to confess 0 Silent is a dominated strategy 0 Nash equilibrium: Confess Confess

26. Prisoners’ Dilemma 0 Each player has a dominant strategy 0 Equilibrium is Pareto dominated 26

27. Elimination of Dominated Strategies 0 Dominated strategy 0 Strategy dominated by another strategy 0 We can solve games by eliminating dominated strategies 0 If elimination of dominated strategies results in a unique outcome, the game is said to be dominance solvable 27

28. 28 (a) Eliminating dominated strategies Player 2 123 Player 1 12, 02, 40, 2 20, 60, 24, 0 (b) One step of elimination Player 2 12 Player 1 12, 02, 4 20, 60, 2 (c ) Two steps of elimination Player 2 12 Player 112, 02, 4

29. 29 (a) Eliminated dominated strategies Player 2 123 Player 1 120, 010, 14, -4 220, 210, 02, -2 (b) Reduced game eliminating column 3 first Player 2 12 Player 1 120, 010, 1 220, 210, 0

30. Games with Many Equilibria 0 Coordination game 0 Players - common interest: equilibrium 0 For multiple equilibria 0 Preferences - differ 0 At equilibrium: players - no change 30

31. 31 Toshiba DOSUNIX IBM DOS600, 200100, 100 UNIX100, 100200, 600 Games with Many Equilibria The strategy pair DOS DOS is a Nash equilibrium as well as UNIX, UNIX

32. Normal Form of Matching Numbers: coordination game with ten Nash equilibria 32 Player 2 12345678910 Player 1 11, 10, 0 2 2, 20, 0 3 3, 30, 0 4 4, 40, 0 5 5, 50, 0 6 6, 60, 0 7 7, 70, 0 8 8, 80, 0 9 9, 90, 0 100, 0 10, 10

33. Table 11.12 A game with no equilibria in pure strategies 33 General 2 RetreatAttack General 1Retreat5, 86, 6 Attack8, 02, 3

34. The “I Want to Be Like Mike” Game 34 Dave Wear redWear blue MichaelWear red(-1, 2)(2, -2) Wear blue(1, -1)(-2, 1)

35. Credible Threats 0 An equilibrium refinement: 0 Analyzing games in normal form may result in equilibria that are less satisfactory 0 These equilibria are supported by a non credible threat 0 They can be eliminated by solving the game in extensive form using backward induction 0 This approach gives us an equilibrium that involve a credible threat 0 We refer to this equilibrium as a sub-game perfect Nash equilibrium. 35

36. 36 Toshiba (DOS if DOS, DOS if UNIX) (DOS | DOS, UNIX | UNIX) (UNIX | DOS, UNIX | UNIX) (UNIX | DOS, DOS | UNIX) IBM DOS600, 200 100, 100 UNIX100, 100200, 600 100, 100 Non credible threats: IBM-Toshiba In normal form 0 Three Nash equilibria 0 Some involve non credible threats. 0 Example IBM playing UNIX and Toshiba playing UNIX regardless: 0 Toshiba’s threat is non credible

37. Backward induction 37 1 2 3 IBM Toshiba UNIX DOS UNIX DOS UNIX DOS 600 200 100 200 600

38. Subgame perfect Nash Equilibrium 0 Subgame perfect Nash equilibrium is 0 IBM: DOS 0 Toshiba: if DOS play DOS and if UNIX play UNIX 0 Toshiba’s threat is credible 0 In the interest of Toshiba to execute its threat

39. Rotten kid game 0 The kid either goes to Aunt Sophie’s house or refuses to go 0 If the kid refuses, the parent has to decide whether to punish him or relent 39 Player 2 (a parent) (punish if the kid refuses) (relent if the kid refuses) Player 1 (a difficult child) Left (go to Aunt Sophie’s House) 1, 1 Right (refuse to go to Aunt Sophie’s House) -1, -12, 0

40. Rotten kid game in extensive form 40 The sub game perfect Nash equilibrium is: Refuse and Relent if refuse The other Nash equilibrium, Go and Punish if refuse, relies on a non credible threat by the parent Kid Parent Refuse Go to Aunt Sophie’s House Relent if refuse Punish if refuse 2020 1111 1 2

41. Application 1: Collusive Duopoly 0 Example: The European voluntary agreement for washing machines in 1998 0 The agreement requires firms to eliminate from the market inefficient models 0 Ahmed and Segerson (2011) show that the agreement can raise firm profit, however, it is not stable Firm 2 eliminateKeep Firm 1 eliminate $1,000 $200$1,200 keep $1,200$200 $500

42. Application 2: Wal-Mart and CFL bulbs market 0 In 2006 Wal-Mart committed itself to selling 1 million CFL bulbs every year 0 This was part of Wal-Mart’s plan to become more socially responsible 0 Ahmed(2012) shows that this commitment can be an attempt to raise profit.

43. 43 1 2 3 Wal-Mart Small firm Do not commit Commit to output target Do not Commit Do not Commit 90 45 500 40 80 60 100 50 When the target is small The outcome is similar to a prisoners dilemma Application 2: Wal-Mart and CFL bulbs market

44. 44 1 2 3 Wal-Mart Small firm Do not commit Commit to output target Do not Commit Do not Commit 80 30 500 35 90 100 50 When the target is large When the target is large enough, we have a game of chicken Application 2: Wal-Mart and CFL bulbs market