Perfect Prediction Equilibrium

Transcript

1. Dr. Ghislain Fourny Stéphane Reiche Prof. Jean-Pierre Dupuy INI, UZH/ETH

   Zürich – Thursday, November 19th, 2015 Perfect Prediction Equilibrium

2. LEIBNIZ AND NASH

3. Leibniz

4. Peter Mary Normal Form

5. Peter Mary Nash Equilibrium

6. Extensive form 1 0 0 2 5 3 3 1

   2 4

7. Extensive form 1 0 0 2 5 3 3 1

   2 4 Node

8. Extensive form 1 0 0 2 5 3 3 1

   2 4 Root

9. Extensive form 1 0 0 2 5 3 3 1

   2 4

10. Extensive form 1 0 0 2 5 3 3 1

    2 4

11. Extensive form 1 0 0 2 5 3 3 1

    2 4

12. Extensive form 1 0 0 2 5 3 3 1

    2 4 Outcome

13. Extensive form 1 4 2 7 3 5 1 7

    2 0

14. NEWCOMB‘S PARADOX

15. 15 Newcomb‘s Paradox

16. 16 Newcomb‘s Paradox $ 1,000 $ 1,000,000 or $ 0

17. 17 Newcomb‘s Paradox: choice 1 $ 1,000 $ 1,000,000 or

    $ 0

18. 18 Newcomb‘s Paradox: choice 2 $ 1,000 $ 1,000,000 or

    $ 0

19. 19 Newcomb‘s Paradox: the catch Long, long, long ago ?

    ?

20. 20 Newcomb‘s Paradox: the catch $ 1,000,000 Long, long, long

    ago

21. 21 Newcomb‘s Paradox: the catch $ 0 Long, long, long

    ago

22. Newcomb‘s Paradox: you choose! $ 1,000 $ 1,000,000 or $

    0

23. Two-boxers‘ reasoning $ 1000

24. Two-boxers‘ reasoning $ x $ x $ 1000

25. Two-boxers‘ reasoning $ x $ x $ 1000 $ x

    +1,000 = = + $ x

26. Two-boxers‘ reasoning $ x $ x $ 1000 = +

    $ x +1,000 = $ x

27. Two-boxers‘ reasoning $ 0 $ 0 $ 0 $ 1000

    $ 1,000 = +

28. One-boxers‘ reasoning $ 1000

29. One-boxers‘ reasoning $ 0 $ 1000 $ 1,000,000

30. One-boxers‘ reasoning $ 0 $ 1000 $ 1,000 $ 1,000,000

    + = = $ 1,000,000

31. One-boxers‘ reasoning $ 0 $ 1000 $ 1,000 $ 1,000,000

    + = = $ 1,000,000

32. Newcomb and Compatibilism • Three topics relevant to this paradox:

    – Free will – Perfect Prediction – Fixity of the past

33. 1 - Free Will The player could have acted otherwise.

    t2 Player does A Player does B

34. 2 – Perfect Prediction In each possible world, the prediction

    is true. t2 Player does C Player does D t1 Prediction of C Prediction of D

35. 3 – Fixity of the past There is nothing that

    the player can do at t2 such that, if he were to do it, P would not have happened. t2 Player does A Player does B t1 Prediction of X Prediction of X

36. All three? t2 t1 ✗

37. (In)compatibilism You can have at most two of these three:

    Free will Perfect Prediction Fixity of the past

38. No game at all • Free will • Perfect Prediction

    • Fixity of the past Player takes n Prediction of n boxes t2 t1 Player takes n Prediction of n boxes

39. Two-boxers • Free will • Perfect Prediction • Fixity of

    the past t2 Player takes 2 Player takes 1 t1 Prediction of 2 boxes Prediction of 2 boxes

40. One-boxers • Free will • Perfect Prediction • Fixity of

    the past t2 Player takes 1 Player takes 2 t1 Prediction of 1 box Prediction of 2 boxes

41. One-boxers • Free will • Perfect Prediction • Fixity of

    the past t2 Player takes 1 Player takes 2 t1 Prediction of 1 box Prediction of 2 boxes Past counterfactually dependent on the future.

42. Causal vs. Counterfactual Misconception: Causal dependency ≠ Counterfactual dependency

43. BACK TO GAME THEORY...

44. Assumptions 1. Extensive Form 1 4 2 7 3 5

    1 7 2 0

45. Assumptions 1. Extensive Form 2. Strict Preferences 3 7 2

    7 ✗

46. Assumptions 1. Extensive Form 2. Strict Preferences 3. Perfect Information

    ✗

47. Assumptions 1. Extensive Form 2. Strict Preferences 3. Perfect Information

    4. No Chance Moves ✗

48. Assumptions 1. Extensive Form 2. Strict Preferences 3. Perfect Information

    4. No Chance Moves 5. Common Knowledge of Rationality

49. Assumptions 1. Extensive Form 2. Strict Preferences 3. Perfect Information

    4. No Chance Moves 5. CK of Rationality 6. CK of outcome, of all decisions, of thought processes 6. Fixity of the past or Nash/Subgame Perfect Equilibrium Perfect Prediction Equilibrium

50. APPETIZER: PROMISE GAME

51. Promise Game 0 0 -1 2 1 1

52. Promise Game 0 0 -1 2 1 1

53. Promise Game 0 0 -1 2 1 1

54. Promise Game 0 0 -1 2 1 1

55. Promise Game: Nash 0 0 -1 2 1 1

56. Promise Game 0 0 -1 2 1 1

57. Promise Game 0 0 -1 2 1 1

58. Promise Game: PPE 0 0 -1 2 1 1

59. GENERAL PRINCIPLES

60. Principles 1 2nd principle: rational bridge 2 ☹ ☺ ✗

    ☺✓ st principle: preemption

61. Self-fulfilling prophecy Outcome Anticipation Causal Dependency Counterfactual Dependency

62. ANOTHER EXAMPLE: TAKE- OR-LEAVE GAME

63. TOL Game 1 0 0 2 5 3 3 1

    2 4

64. TOL Game 1 0 0 2 5 3 3 1

    2 4

65. TOL Game 1 0 0 2 5 3 3 1

    2 4

66. TOL Game 1 0 0 2 5 3 3 1

    2 4

67. TOL Game: Nash 1 0 0 2 5 3 3

    1 2 4

68. TOL Game 1 0 0 2 5 3 3 1

    2 4

69. TOL Game 1 0 0 2 5 3 3 1

    2 4 1

70. TOL Game 1 0 0 2 5 3 3 1

    2 4 2

71. TOL Game 1 0 0 2 5 3 3 1

    2 4 2

72. TOL Game 1 0 0 2 5 3 3 1

    2 4 1

73. TOL Game 1 0 0 2 5 3 3 1

    2 4 2

74. TOL Game: PPE 1 0 0 2 5 3 3

    1 2 4 2

75. CONCLUSIVE REMARKS

76. Take-Home Message Nash Fixity of the past PPE CK of

    the outcome of the game

77. Theorems Theorem 1 The Perfect Prediction Equilibrium exists and is

    unique. Theorem 2 The Perfect Prediction Equilibrium is Pareto-Optimal.

78. Picture Copyright: hypermania2, merznatalia, sereznyi, shtanzman, denispc / 123RF Stock

    Photo