Games Economists Play!

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Games Economists Play!

  1. 1. ZtÅxá Ç XvÉÇÉÅ|vá Based on The Book The Law and Economics By Charles J Joetz http://people.virginia.edu/~cjg4t/le/Materials/Law%20and%20Economics%200106.pdfWali Memon December 27, 2010 1
  2. 2. The Prisoners’ Dilemma O A simple game that has become the dominant paradigm for social scientists since it was invented about 1960. O How the game works -- a simple narrative.Wali Memon December 27, 2010 2
  3. 3. PD games help to explain why we do dumb things O Over-fish lakes and oceans O Pollute O Arms race O Fail to exploit bargaining gainsWali Memon December 27, 2010 3
  4. 4. Modeling PD games O Game theoretic problems: payoffs for each player depend on actions of both Wali Memon December 27, 20104
  5. 5. Hollywood gets in the act Russell Crowe as John Nash in “A Beautiful Mind” Wali Memon December 27, 20105
  6. 6. The need for poetic license Wali Memon December 27, 20106
  7. 7. Modeling PD games O Game theoretic problems: payoffs for each player depend on actions of both O Two possible strategies: A party cooperates when he performs value-increasing promises, and defects when he breaches Wali Memon December 27, 20107
  8. 8. Modeling Two-party choice CooperatePlayer 1 Wali Memon December 27, 2010 8
  9. 9. Modeling Two-party choicePlayer 1 Defect Wali Memon December 27, 2010 9
  10. 10. Modeling Two-party choice: Player 2 Player 2 CooperateWali Memon December 27, 2010 10
  11. 11. Modeling Two-party choice: Player 2 Player 2 DefectWali Memon December 27, 2010 11
  12. 12. Modeling Two-party Choice: Both Cooperate Player 2 Cooperate Defect Both Cooperate cooperatePlayer 1 Defect Wali Memon December 27, 2010 12
  13. 13. Modeling Two-party Choice: Both Defect Player 2 Cooperate Defect CooperatePlayer 1 Defect Both defect Wali Memon December 27, 2010 13
  14. 14. Modeling Two-party Choice Player 2 Cooperate Defect Player 1 cooperates, Cooperate Player 2Player 1 defects Defect Wali Memon December 27, 2010 14
  15. 15. Modeling Two-party Choice Player 2 Cooperate Defect CooperatePlayer 1 Player 1 defects, Defect Player 2 cooperates Wali Memon December 27, 2010 15
  16. 16. Modeling Two-party Choice Player 2 Cooperate Defect Player 1 Both cooperates, Cooperate cooperate Player 2Player 1 defects Player 1 defects, Defect Both defect Player 2 Wali Memon cooperates December 27, 2010 16
  17. 17. Let’s examine Joint Cooperation Player 2 Cooperate Defect Both Cooperate cooperatePlayer 1 Defect Wali Memon December 27, 2010 17
  18. 18. Joint Cooperation: Omerta as a substitute for contracting I’mThe food is worried better at about the Tessio…Tattaglias… Wali Memon December 27, 2010 18
  19. 19. Joint Defection Player 2 Cooperate Defect CooperatePlayer 1 Defect Both defect Wali Memon December 27, 2010 19
  20. 20. Joint defection: Can these gentlemen be acting efficiently?Wali Memon December 27, 2010 20
  21. 21. Player 1: Sucker’s Payoff Player 2 Cooperate Defect Player 1 cooperates, Cooperate Player 2Player 1 defects Defect Wali Memon December 27, 2010 21
  22. 22. Sucker’s payoff: Sucker performs, other party defects GONERIL Hear me, my lord; What need you five and twenty, ten, or five, To follow in a house where twice so many Have a command to tend you? REGAN What need one? KING LEAR O, reason not the need…Wali Memon December 27, 2010 22
  23. 23. Player 1: Defector’s Payoff Player 2 Cooperate Defect CooperatePlayer 1 Player 1 defects, Defect Player 2 cooperates Wali Memon December 27, 2010 23
  24. 24. Defector’s Payoff: Defector breaches, sucker performs "I can make them voting machines sing Home Sweet Home." "Dont write anything you can phone. Dont phone anything you can talk. Dont talk anything you can whisper. Dont whisper anything you can smile. Dont smile anything you can nod. Dont nod anything you can wink." Gov.Memon K. Long Wali Earl December 27, 201024
  25. 25. Let’s apply this to promising Player 2 Cooperate Defect Both Player 1 gets Cooperate cooperate: sucker’s Omerta payoff: LearPlayer 1 Player 1-- defector’s Both defect: Defect payoff: Gov. The duelists Earl Wali Memon December 27, 2010 25
  26. 26. Modeling Promisor Choices Player 2 Cooperate Defect Player 2 Both breaches, Cooperate promise andPlayer 1 Player 1 perform performs Player 1 Both defect: performs, Defect No one player 2 breaches performs Wali Memon December 27, 2010 26
  27. 27. Plugging in payoffs First number is payoff for Player 1, Second number is payoff for Player 2 Player 2 Cooperate Defect Cooperate 3, 3 -1, 4Player 1 Defect 4, -1 0, 0 Wali Memon December 27, 2010 27
  28. 28. Defection dominates for Player 1 Cooperate Defect Cooperate 3 -1Player 1 ↓ ↓ Defect 4 0 Wali Memon December 27, 2010 28
  29. 29. Defection dominates for Player 2 Player 2 Cooperate Defect Cooperate 3 4 ↓ ↓ Defect -1 0Wali Memon December 27, 2010 29
  30. 30. Defection dominates: Goetz pp. 10-11 Cooperate Defect Cooperate a cPlayer 1 ↓ ↓ Defect b d Wali Memon December 27, 2010 30
  31. 31. I am always better off if the opponent cooperates: Goetz pp. 10-11 Cooperate Defect ↓ ↓ ↓ ↓ Cooperate a cPlayer 1 ↓ ↓ ↓ ↓ Defect b dWali Memon December 27, 2010 31
  32. 32. a+a is greater than any other summation of payoffs Player 2 Cooperate Defect Cooperate a+a c+c Defect b+b d+dWali Memon December 27, 2010 32
  33. 33. The paradox of the PD game O While cooperation is collectively rational, defection is individually rational. Wali Memon December 27, 201033
  34. 34. The paradox of the PD game O While cooperation is collectively rational, defection is individually rational. O The undersupply of cooperation is “the tragedy of the commons.” Garrett Hardin, The Tragedy of the Commons (1968). Wali Memon December 27, 201034
  35. 35. The Tragedy of the Commons and the Law of the Sea Wali Memon December 27, 2010 35)
  36. 36. An application from David Hume: Your corn is ripe today, mine will be so tomorrow… Wali Memon December 27, 2010 36Treatise on Human Understanding III.ii.V (1739)
  37. 37. University vs. Eager Goetz p. 7 Wali Memon December 27, 201037
  38. 38. University v. Eager: Goetz p. 7 How would you plug in the payoffs? Player 2 Cooperate Defect CooperatePlayer 1 Defect Wali Memon December 27, 2010 38
  39. 39. University v. Eager Joint Defection: Everyone cheats and Exam does not signal any useful information Player 2 Cooperate Defect CooperatePlayer 1 Defect 0,0 Wali Memon December 27, 2010 39
  40. 40. University v. Eager Joint Cooperation: No one cheats and exam measures true performance Player 2 Cooperate DefectPlayer 1 Cooperate ?,? Defect Wali Memon December 27, 2010 40Ex ante, are the positions symmetrical?
  41. 41. University v. Eager Sucker’s Payoff when one cooperates and the other defects Player 2 Cooperate Defect Cooperate ?,?Player 1 Defect ?,? Wali Memon December 27, 2010 41 Will only the cheater get into med school?
  42. 42. University vs. Eager Goetz p. 7 Wali Memon December 27, 201042
  43. 43. Is the university at fault? O An irresistible temptation? O Is the penalty too high? How would you set it? Wali Memon December 27, 201043
  44. 44. The game of chicken Wali Memon December 27, 201044
  45. 45. Turning a PD game into a Chicken game. What happens when joint defection is really bad? Player 2 Cooperate Defect Cooperate 3, 3 -1, 4Player 1 Defect 4, -1 Wali Memon December 27, 2010 45
  46. 46. Turning a PD game into a Chicken game. What happens when joint defection is really bad? Player 2 Cooperate Defect Cooperate 3, 3 -1, 4Player 1 Defect 4, -1 -∞, -∞ Wali Memon December 27, 2010 46
  47. 47. Turning a PD game into a Chicken game. Defection no longer dominates Player 2 Cooperate DefectPlayer 1 Cooperate 3, 3 -1, 4 Defect 4, -1 -∞, -∞ Wali Memon December 27, 2010 47
  48. 48. Turning a PD game into a Chicken game. It might not be so drastic Player 2 Cooperate Defect Cooperate 3, 3 -1, 4Player 1 Defect 4, -1 -6, -6 Wali Memon December 27, 2010 48
  49. 49. Can you think of applications? Wali Memon December 27, 201049
  50. 50. Can you think of applications? The Chicken Game: the Canadian contribution to NATO ca. 1970 Wali Memon December 27, 201050
  51. 51. Military spending during the Cold War as a Chicken Game Player 2 Cooperate Defect All parties Player 1 a make a fair Cooperate sucker, PlayerPlayer 1 military 2 cheats contribution Player 1 Soviets Defect cheats, Player invade 2 a sucker Wali Memon December 27, 2010 51
  52. 52. Here’s another game: The Coordination Game Player 2 1,1 0,0 Gives examples of thisPlayer 1 0,0 1,1 Wali Memon December 27, 2010 52
  53. 53. Battle of the sexes as a variant of Coordination Games Wife Boxing Match Opera Boxing Match 3,1 0,0Husband Opera 0,0 1,3 Wali Memon December 27, 2010 53
  54. 54. PD Games and externalities Goetz p. 11 O How one acts affects other parties, for good or ill O These third party effects are called externalities Wali Memon December 27, 201054
  55. 55. Externalities may be good or bad An external bad… Wali Memon December 27, 201055
  56. 56. Externalities may be good or bad External goods Wali Memon December 27, 201056
  57. 57. Question 4, page 13:Urban renewal What kind of a game is this? Player 2 Cooperate Defect CooperatePlayer 1 Defect Wali Memon December 27, 2010 57
  58. 58. Question 4, page 13:Urban renewal What kind of a game is this? Player 2 Cooperate Defect Both CooperatePlayer 1 beautify Defect Neither do Wali Memon December 27, 2010 58
  59. 59. Question 4, page 13:Urban renewal One possible game: everyone beautifies their garden Player 2 Cooperate Defect Cooperate 3,3 2,1Player 1 Defect 1,2 0,0 Wali Memon December 27, 2010 59
  60. 60. Question 4, page 13:Urban renewal Cleaning the commons as a chicken game Player 2 Cooperate Defect Cooperate 3,3 -1,1Player 1 Defect 1,-1 0,0 Wali Memon December 27, 2010 60
  61. 61. Suppose your neighbors have organized a “clean-up day” for the commons O Can you think of some excuses you might give your neighbors not to participate? O Would you expect other neighbors to come up with the same excuses? O What might militate against such excuses? Wali Memon December 27, 201061
  62. 62. Can social sanctions solve the incentive problem? O Consider the following examples of cooperative behavior: O Not littering O Showing up one time when one has agreed to meet a friend O Not betraying a friend O Helping out in an emergency: the Good Samaritan O Loyalty in wartime Wali Memon December 27, 201062
  63. 63. Can social sanctions solve the incentive problem? O What changes when the game is repeated (or “iterated”) O Are there such things as high-trust and low- trust societies? Do some societies have a general tradition of keeping agreements? Wali Memon December 27, 201063

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