Perfect Prediction Equilibrium

Perfect Prediction Equilibrium

Presented in Interlaken on Monday, July 17. Great discussions with other researchers working on non-Nashian solution concepts.

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Ghislain Fourny

July 20, 2017
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  1. Ghislain Fourny ETH Zürich ASIC – Interlaken – Monday, July17th,

    2017 Perfect Prediction Equilibrium Stéphane Reiche Mines ParisTech Jean-Pierre Dupuy Stanford University
  2. COUNTERFACTUALS IN GAMES

  3. Peter Mary Normal Form

  4. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Prisoner's dilemma
  5. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Peter's best response
  6. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Peter's best response
  7. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Peter's best response
  8. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Peter's best response
  9. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Peter's best response
  10. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Peter's best response
  11. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Peter's best response
  12. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Nash equilibrium (1951)
  13. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Dependent strategies
  14. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Dependent strategies
  15. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Dependent strategies
  16. Peter Mary Defect Cooperate Defect 1,1 3,0 Cooperate 0,3 2,2

    Hofstadter equilibrium (1983)
  17. Causal vs. Counterfactual Misconception: Causal dependency ≠ Counterfactual dependency

  18. Non-Nashian solutions Nashian Super-Nashian Counter-Nashian Normal form Nash Equilibrium (Nash)

    Rationalizability (Bernheim, Pearce) (Perfect) Cooperative Equilibrium (Rong, Halpern) Superrationality (Hofstadter) Minimax- Rationalizability (Halpern, Pass) Individual Rationality (Halpern, Pass) Extensive form Subgame Perfect Equilibrium (Selten) Joint-Selfish-Rational Equilibrium (Shiffrin) Perfect Prediction Equilibrium (Fourny, Reiche, Dupuy)
  19. Extensive form 1 4 2 7 3 5 1 7

    2 0 Node Root Outcome
  20. Prediction conundrum Always predicts correctly Has free choice vs.

  21. NEWCOMB'S PROBLEM

  22. 22 Newcomb‘s Paradox $ 1,000 $ 1,000,000 or $ 0

  23. 23 Newcomb‘s Paradox: choice 1 $ 1,000 $ 1,000,000 or

    $ 0
  24. Newcomb‘s Paradox: choice 2 $ 1,000 $ 1,000,000 or $

    0
  25. 25 Newcomb‘s Paradox: the catch $ 1,000,000 Long, long, long

    ago $ 0 Or
  26. Newcomb‘s Paradox: you choose! $ 1,000 $ 1,000,000 or $

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

    +1,000 = = + $ x
  28. Two-boxers‘ reasoning $ 0 $ 0 $ 1000 $ 1,000

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

    + = = $ 1,000,000
  30. (In)compatibilism You can have at most two of these three:

    Free will Perfect Prediction Fixity of the past
  31. Two-boxers • Free will • Perfect Prediction • Fixity of

    the past Player takes 2 Player takes 1 Prediction of 2 boxes Prediction of 2 boxes t2 t1 Ad-hoc prediction
  32. One-boxers • Free will • Perfect Prediction • Fixity of

    the past Player takes 1 Player takes 2 Prediction of 1 box Prediction of 2 boxes t2 t1 Perfect prediction
  33. One-boxers • Free will • Perfect Prediction • Fixity of

    the past Player takes 1 Player takes 2 Prediction of 1 box Prediction of 2 boxes t2 t1 Past counterfactually dependent on the future. Perfect prediction
  34. Prediction semantics Ad-hoc prediction Perfect prediction vs. profactual counterfactual

  35. ASSUMPTIONS

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

    1 7 2 0
  37. Assumptions 1. Extensive Form 2. Strict Preferences 3 7 2

    7 ✗
  38. Assumptions 1. Extensive Form 2. Strict Preferences 3. Perfect Information

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

    4. No Chance Moves ✗
  40. Assumptions 1. Extensive Form 2. Strict Preferences 3. Perfect Information

    4. No Chance Moves 5. Common Knowledge of Rationality
  41. 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 Perfect prediction Ad-hoc prediction
  42. PROMISE GAME

  43. Promise Game 0 0 -1 2 1 1

  44. Promise Game 0 0 -1 2 1 1

  45. Promise Game 0 0 -1 2 1 1

  46. Promise Game 0 0 -1 2 1 1

  47. Promise Game 0 0 -1 2 1 1

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

  49. Promise Game 0 0 -1 2 1 1

  50. Promise Game 0 0 -1 2 1 1

  51. Promise Game 0 0 -1 2 1 1

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

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

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

  55. GENERAL PRINCIPLES

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

    ☹ ☺✓ st principle: preemption
  57. Self-fulfilling prophecy Outcome Anticipation Causal Dependency Counterfactual Dependency

  58. ANOTHER EXAMPLE: TAKE-OR-LEAVE GAME

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

    2 4
  60. TOL Game 1 0 0 2 5 3 3 1

    2 4
  61. TOL Game 1 0 0 2 5 3 3 1

    2 4
  62. TOL Game 1 0 0 2 5 3 3 1

    2 4
  63. TOL Game: Nash 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 1
  66. TOL Game 1 0 0 2 5 3 3 1

    2 4 2
  67. TOL Game 1 0 0 2 5 3 3 1

    2 4 2
  68. TOL Game 1 0 0 2 5 3 3 1

    2 4 1
  69. TOL Game 1 0 0 2 5 3 3 1

    2 4 2
  70. TOL Game: PPE 1 0 0 2 5 3 3

    1 2 4 2
  71. CONCLUDING REMARKS

  72. Take-Home Message Nash/Selten Fixity of the past PPE CK of

    the outcome of the game
  73. Theorems Theorem 1 The Perfect Prediction Equilibrium exists and is

    unique. Theorem 2 The Perfect Prediction Equilibrium is Pareto-Optimal.
  74. Algorithmic complexity O(nd) number of nodes depth Quadratic (Any number

    of players)
  75. Picture Copyright: hypermania2, merznatalia, sereznyi, shtanzman, denispc / 123RF Stock

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

    – Free will – Perfect Prediction – Fixity of the past
  77. 1 - Free Will The player could have acted otherwise.

    t2 Player does A Player does B
  78. 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
  79. 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
  80. All three? t2 t1

  81. 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