FIRST: THE INSPECTION GAME 2 UNCERTAINTY: Employee does not know - - PDF document

And The Link With Theory Of Mind CLASS 8

STRATEGIC THINKING IN GAMES AND MARKETS

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FIRST: THE INSPECTION GAME

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UNCERTAINTY:

• Employee does not know what employer will do
• Employer does not know what employee will do

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PREDICTING UNDER THIS UNCERTAINTY

• This skill is extremely important in modern economic life
• Yet we don’t understand why (many) humans are good at it
• Humans seem to apply the right “intuition”
• Who?
• What is this intuition?

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NASH

• Subjects do not play the equilibrium strategies from the one-shot

game

• So, forecasting what the opponent will do cannot be based on this

prediction

• (Of course, you can try to figure out the Nash equilibrium of the

multi-stage game, but there are lots, lots,...)

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PSYCHOLOGISTS TALK ABOUT: THEORY OF MIND

• “Theory of Mind” (or “mentalizing”) is the ability to recognize and

understand intentions or goal-directness in patterns in one’s environment

• … as opposed to mere expression of physical laws
• Intention:
• Malevolent
• Benevolent
• Involves (“new”) regions of the cortex, distinct from formal

mathematical and probabilistic brain regions

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Example: The intentional stance of a moving object Base Situation New Situation 1 Physics OK New Situation 2: ?!

(Uller, Nichols, Cognition, 2000)

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REMARKS

• One-year old infant (and apes) may be able to recognize goal-

directness but cannot use it to its advantage (E.g., chocolate-in- drawer experiment)

• But:
• What does Theory of Mind mean formally?
• Enter Economics…

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THEORY OF MIND ENGAGES PART OF THE “SOCIAL BRAIN”

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IN GAMES:

• Recently, Theory of Mind brain

regions have been found to be activated also when playing strategic games

• … such as rock, paper, scissors

(Gallager-Frith, 2003: contrast between playing against human and against simple computer- based rule)

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BUT…

• These are simple contrasts (affectionately called “blobology”)
• What computations are involved?

Hampton, Bossaerts, O’Doherty, PNAS, 2008

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MATHEMATICS: REINFORCEMENT LEARNING

Prediction Error Action Value Logit Model for Probability of Action a

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MATHEMATICS: FICTITIOUS PLAY

Stochastic (Logit) Best Response Given Beliefs Learning of Opponent’s Strategy Prediction Error

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MATHEMATICS: “INFLUENCE”

Taylor Expansion of Strategies Getting Opponent’s Beliefs Learning From Action Of Opponent (“Fictitious Play”) Predicted Change In Opponent Actions (“Influence”)

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THE REWARD ERROR FROM THE “INFLUENCE” PREDICTION IS ENCODED IN PCC:

Hampton, ea, PNAS 2008

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(HERE IS THE FICTITIOUS PLAY REWARD PREDICTION ERROR:)

Striatum: Traditionally involved in reinforcement learning (Based on “dopamine”)

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DIFFERENCE WITH CLASSICAL GAME THEORY:

• (Static) Nash equilibrium predicts:
• Employee works with probability 1/5; shirks with probability 4/5
• Employer inspects with probability 1/2
• No need to predict effect of own actions on opponent’s beliefs and

actions!

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RELATED TO HIGHER-ORDER THINKING

NO correlation with accuracy in the calculation task (r = .009, P >.5) Coricelli and Nagel (2009)

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STAG-HUNT

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• Complex stag-hunt game
• Against sophisticated (order

k) computer

• E.g., Order 2 = “I think that

you think that I will move left”

• (Cooperation, i.e., stag hunt,

increases when order k increases)

UNCERTAINTY ABOUT INFERENCE OF COMPUTER’S LEVEL IS ENCODED IN MPFC (YOSHIDA EA)

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OWN LEVEL OF K CORRELATES WITH NEURAL ACTIVITY

• Lateral PFC, Superior Parietal Lobule, Superior Frontal Sulcus

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COMPARING AUTISTIC PATIENTS WITH CONTROLS

• Patients cannot track changes in

sophistication (order k) of computer

• Model that assumes fixed k for

computer fits choices better than model that tracks changes in k (“ToM model”)

• Equivalently: “forgetting

rate” (discarding old observations) is higher for controls

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(ANALOGOUS EFFECTS IN TRUST GAME FOR BORDERLINE PERSONALITY DISORDER PATIENTS)

• King Cases ea: When trust is broken in trust game, BPD patients

cannot re-establish trust

• Related to different activation in anterior insula (they do not expect

trust to go away, but once it does, they don’t know anymore what world they live in

• COMPUTATIONAL (NEURO)PSYCHIATRY

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TOWARDS “MANIPULATION”

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• Bhatt ea, PNAS (2010)
• Beyond influence (taking into account that one is learning about a moving

target)

• Really “teaching” (belief manipulation)

OF INCREMENTALISTS, STRATEGISTS AND RATIONALISTS

• Incrementalists: correlate

price suggestion with value

• Rationalists: think everyone

is rational, and induce no correlation in relation with value...

• Strategist: react to

presence of incrementalists by anti-correlating suggested price and value!

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IQ, SOCIOECONOMIC STATUS AND EARNINGS

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IMAGING

• Differential activation for strategists

(between-group comparison)

• Compare to

Yoshida’s imaging results!

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NEXT: FINANCIAL MARKETS WITH “INSIDERS”

• Even large-scale, anonymous financial markets may be perceived as

intentional, goal-oriented – or “strategic:” there may be “insiders”

• Questions:

1.

Is this within scope of Theory of Mind?

2.

Does Theory of Mind help?

3.

What does it do?

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EXPERIMENT:

• Markets are re-played in scanner while subject is exposed to risk
• Subject:
• Predicts price changes in market replay;
• Performs Theory of Mind tests;
• Performs (financial) mathematics test

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MARKET REPLAY

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Graphical replay of market

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IMAGING RESULTS

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Effect of |price-0.25|, contrast between insider and no-insider treatment Bruguier, ea, J Finance 2010

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EXPLANATORY VARIABLES FOR BRAIN ACTIVATION

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PREDICTION PERFORMANCE RESULTS

Against Heider test

2 4 6 8 10 12 14 45 50 55 60 65 70 75 80 85 !=0.348247, p=0.022110, n=43 Heider Test Financial Market Prediction

Against Math test

−1 1 2 3 4 5 6 7 8 45 50 55 60 65 70 75 !=0.060792, p=0.698569, n=43 Mathematical puzzles Financial Market Prediction

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WHAT DOES THIS MEAN FORMALLY?

! Theory of Mind brain regions are engaged and financial

performance correlates with Theory of Mind skills

! Now, Theory of Mind = pattern recognition ! So: What patterns are attended to? ! First of all: What distinguishes presence of insiders?

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PRICING PATTERNS WHEN THERE ARE INSIDERS: VOLATILITY CLUSTERING

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“GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY” (GARCH)

! Typical autocorrelations of absolute price change: GREEN=Insiders;

BLUE=No Insiders

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(CONTRAST WITH ECONOMIC THEORY)

! Rational Expectations Equilibrium: Uninformed

are supposed to know how prices relate to information

• f insiders

! Where does this knowledge come from?! ! Here we provide a partial answer

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ASSET PRICE BUBBLES

• Similar activations when there is mis-pricing...

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TAKE-HOME MESSAGES I

! Playing strategic games engages “Theory of Mind” ! Theory of Mind is about predicting how the opponent

changes strategies because she is learning

! Goes beyond fictitious play and reinforcement learning

(opponent is intentional)

! Theory of Mind is mathematics: pattern recognition ! … which is not the mathematics of Nash equilibrium

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TAKE-HOME MESSAGES II

! Theory of Mind also applies to understanding “social

systems” that don’t really have a mind on their own

! We see this in brain activation when exposed to risk in

markets with insiders

! We also see this in correlation of performance

between predicting prices in such markets and traditional Theory of Mind tasks

! … and in the absence of correlation with

mathematical skill (as when playing strategic games)

! Patterns being recognized = GARCH?

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