Ghislain Fourny
November 19, 2015

Perfect Prediction Equilibrium

Talk given on Thursday 19 November 2015
at the Institut für Neuroinformatik,
Universität Zürich/ETH Zürich.

Ghislain Fourny

November 19, 2015

Transcript

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

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

2 4

2 4 Node

2 4 Root

2 4

2 4

2 4

2 4 Outcome

2 0

\$ 0

\$ 0

?

ago

ago

0

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

+1,000 = = + \$ x
26. Two-boxers‘ reasoning \$ x \$ x \$ 1000 = +

\$ x +1,000 = \$ x

\$ 1,000 = +

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

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.

1 7 2 0

7 ✗

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

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

☺✓ st principle: preemption

2 4

2 4

2 4

2 4

1 2 4

2 4

2 4 1

2 4 2

2 4 2

2 4 1

2 4 2

1 2 4 2

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.

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