Intuition and Deliberation

- Two Systems for Strategizing in the Brain

Duo-process theory distinguishes between intuition and reasoning.

Intuition (system 1): fast and emotional

Reasoning (system 2): slow and controlled

These differences imply different games might be fundamentally

different.

coordination games vs. dominance solvable games

dominance solvable games

prisoner’s dilemma game

Confess

Don’tconfess

Confess 2,2 4,0

Don’tconfess

0,4 3,3eliminate

iterated elimination of dominated strategies

Confess

Don’tconfess

Confess 2,2 1,0

Don’tconfess

0,4 3,3eliminate (second)

eliminate (first)

Games that can be solved by iterated elimination is called dominance

solvable games.

Notice that computers can be very good at dominance solvable games, maybe even

better than human.

Coordination games are very different.

Meeting in NY game

GrandCentral

EmpireState

GrandCentral

1,1 0,0

EmpireState

0,0 1,1

There is nothing to eliminate.

Computers may be very bad at it but human may be better.

Studies on coordination games are few.

Mehta et al (AER, 1994) asked subjects to name one color, one number and one year.

•When subjects were not rewarded based on their answers, they…

•When subjects were rewarded if they said the same thing as their randomly assigned partners,

they…

•When subjects were not rewarded based on their answers, blue and red turned out to be equally

popular (35% each), the most popular number was 7 (11%) and the current year was named 6.8% of

times.

•When subjects were rewarded if they said the same thing as their randomly assigned partners, 58.9% people named red, 40% of people chose

number 1 and the 61.1% named the current year.

In Schelling’s terms, the color red, the number 1 and the current year are focal

points.

•What exactly focal points are and how do people reach a focal point partly motivate this study.

•We would like to study both the behavioral and neural difference between dominance solvable and

coordination games.

Compare coordination games with dominance solvable games:

There is nothing to eliminate.Computers may be very bad at it but

human may be better.

Methodology: We scanned 21 subjects in an fMRI scanner when they were making choices in dominance solvabl

e and coordination games.•We would like to know the natural reaction of subjects so only subjects who have never taken any

game theory course were recruited.

•Moreover, no feedback was given inside the scanner.

•21 is a good sample size.

Most importantly, the payoff matrix is hard to grasp (we cannot do it without paper and pen and it is not a good reason if equilibrium fails just because people have difficulties in understanding the payoff matrix rather than in figuring out an equilibrium), so we use the following new design of box games

and number games. 2 treatments: box and number2 conditions: domi and coor

The following are some sample screens that subjects saw.

you ： 1R

other ： 1R 1U

ABC

2 3ABC

1

ABC

2 3ABC

1

you ： other

other ： you

1

You ： 0 1 2 3

Other ： 0 1 2 3

you ： other + 1

other ： you

You ： 0 1 2 3

Other ： 0 1 2 3

you ： other

other ： you

Let us now solve for the two sample dominance solvable games. Thank god there is nothing to solve for coordination games.

you ： one rightother ： one right one up

you ： other + 1

other ： you

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3

0 1 2 3 0 1 2 3

Some of our subjects do like this (go back and forth between herself and the other).

The point is it is easier to do elimination by eyes for these games.

you ： one rightother ： one right one up

● ● ● ●●

0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3

0 1 2 3 you ： other + 1

other ： you

● ●

●

● ●

Now let us go back to the sample coordination games. See how the answers “pop out.”

Our fMRI subjects (21) respond by:

Our pilot subjects (41) respond by:

Domi Coor

1 1(3)

16(e)(32)

(1)2

(4)

(1)

3(1)

18(33) (2)

(4)

Domi Coor

0 1 2 3 0 1 2 3

1 1 1 18 18 2 1 0 (e)

(1 5 2 33 12 8 14 4)

According to Schelling, focal points “have symbolic or connotative characteristics that transcend the mathematical structure of the game.” We have some interesting sample questions in this respect.

You: 747 767 380 757

Other: 747 767 380 757

You: 911 228 921 124

Other: 911 228 921 124

ABCD

2 3 4ABCD

11

Cooror

Domi

Cooror

Domi

Cooror

Domi

experiment design and time line: event related and self-paced

Now we know the games, we turn to the fMRI (functional magnetic resonance imaging).

a typical EPI image a scanner

When neurons fire, blood releases oxygen to them at a greater rate than to inactive neurons. Since oxyhemoglobin and deoxyhemoglobin have different magnetic susceptibility, this magnetic signal variat

ion can be detected using an MRI scanner.

Given many repetitions of a thought, action or experience, statistical methods can be used to determine the areas of the brains which have more of this difference as a result, and therefore which areas of brains are active during that thought, action or exp

erience.

excitationexcitation receptionreception

MR

sig

nal (S

)

activeactive

resting resting

TE t

experiment parameters

Slice 25, FOV read 256, FOV Phase 100

Slice Thickness: 4mm

TR: 2000 ms

TE: 34 ms

Phase Oversampling: 38

Base Resolution: 64

Phase Resolution: 100

In a nutshell, we estimate a general linear model.

Signal = bd[Domi]+bc[Coor]+bm[Motor]+ε and we run t-tests on bd - bc and bc- bd.

First, let us look at our behavioral data.

reaction time expected payoff avg. payoffagainst mode

Coor 9.78 sec (2.90) 46.10% (18%) 69.92% (18%)

Domi 35.81 sec (15.98) 66.97% (21%) 79.26% (21%)

Pro

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ion

of p

artic

ipan

ts c

hoos

ing

the

uniq

ue p

redi

ctio

n or

the

mod

al c

hoic

e

0.0

0.2

0.4

0.6

0.8

1.0

Dominance SolvableCoordination

Number-Game Grand TotalBox-Game

Ave

rage

of p

artic

ipan

ts'

expe

cted

pay

offs

0.0

0.2

0.4

0.6

0.8

1.0

Dominance SolvableCoordination

Number-Game Grand TotalBox-Game

Ave

rage

res

pons

e tim

es (

secs

)

0

10

20

30

40

50

60

70

Dominance SolvableCoordination

Number-Game Grand TotalBox-Game

Two observations can be drawn from the behavioral data.

•Humans are really different from computers (esp in Coor games). If we test whether subjects’ choices are random by Pearson test, the p-value is 0.00 (0.00 for Coor). So they are not choosing randomly. Bootstrapping the distribution of expected payoffs shows that the p-value of the expected payoff of

a randomizer is 0.00.

•They take longer time to make choices in Domi games than in Coor games.

The difference in reaction time complicates data analysis.

One can argue that the difference we see in bd – bc and bc- bd results from the difference in reaction time instead of the difference in

nature of these two types of games.

To address this, we run three other regressions. In one, the “task” regressor is parametrically modulated by reaction time. In another, reaction time is incorporated as other regressors (which do not convolve with HRF). In the third, we only model the first 8 se

conds of each trial.

These three regressions give very similar results.

Let first review some basics about the brain.

Coor-Domi (bc- bd)Domi-Coor (bd- bc)

In short, in Domi-Coor, we find activation in fronto-parietal network (the middle frontal gyrus, the inferior parietal lobule, precun

eus).

On the other hand, in Coor-Domi we consistently find activation in insula and ACC.

Domi-Coor Coor-Domi

What exactly do these results mean?

Domi-Coor: working memory

Coor-Domi: salience detection

Fronto-parietal activation results when tasks require attention, conscious perception, reasoning and m

emorizing.

Domi-Coor

Previous literature: fronto-parietal activity observed when contrasting logical reasoning to tasks where reasoning is not r

equired,when contrasting challenging reasoning tasks to st

raightforward ones,or when contrasting a meaningful middle game po

sition to a random game position.

Dominance solvable games may induce players to go through steps of reasoning. In each step, players may need to eliminate some choices and memori

ze.

Domi-Coor

Verbally encode and hold the targets of both: Inferior parietal lobule is implicated in verbal memory

storage.

Eliminating dominated strategies may engage the central executive which is to manipulate the contents of storage: Middle frontal gyrus is thought to e

xecute goal-directed operations.

Keeping track of which strategies are eliminated may require generating and retrieving a mental image: Precuneus may be related to memory retrieval

and imagery.

Domi-Coor

The greater fronto-parietal activation in dominance solvable games is consistent with the hypothesis that these areas assist in step-by-step deliberative

mental processes.

One anecdote is this. The parietal lobe of Einstein’s brain was 15 percent larger than average. Maybe

that is why he is smart?

Domi-Coor

Insula: implicated in subjective pre-reflective and reflective representations of ongoing changes in in

ternal bodily and feeling states.

Insula receives information from receptors in the skin and in internal organs. If an animal is hot, it seeks shade. If hungry, it looks for food. If hurt, it li

cks the wound.

ACC: a conflict monitor when tasks require attention, novel or open-ended responses or when cogniti

ve uncertainty exists.

Coor-Domi

Previous literature:

When participants contemplate cooperating instead of competing with another person,

when they judge other persons to be trustworthy instead of being untrustworthy,

or when they experience social emotions suchas empathy or love, insula and ACC activate.

These emotions might have evolved to ensurequick responses to the factors arousing them in the

presence of many stimuli.

Coor-Domi

Many social interactions involve myriad stimuli but demand immediate decisions.

Rapid processing and extraction of the most salient aspects of complex situations is

characteristic of intuitive decision making.

Complex: multi-purpose, respond to many factors and be flexible

Quick processing: extract the most salient feature

Coor-Domi

The insula and ACC seem to be part of a general network contributing to a

quick and exible evaluation of complex multi dimensional experiences.

In our experiment, deciding within the

context of a coordination game which Nash equilibrium has the most salient

characteristics requires rapid processing of various cultural connotations as

well as geometric symmetry, centrality or even mathematical oddity.

Coor-Domi

The middle insula receives inputs regarding the

physiological condition of the body from the posterior insula and integrates

this with salient environmental stimuli.

The posterior insula and the

SMA/CMA are shown to be responsive to changes of many sensory modalities, whereas the anterior i

nsula and ACC are sensitive to novelty.

Coor-Domi

The key to coordination may be the ability to make judgments of salience common to both. That is, the participant must identify features which are likely to be salient not only to herself but also to the ot

her.

The previous studies all point to a possible role of insula and ACC in identifying salience and provide support for the hypothesis that the higher activation we observe is due to participants extracting sali

ent features in order to coordinate.

Coor-Domi

Post-scan interviews indicated that many used intuitions or “gut feelings” to identify the focal points of coordination games. They just know how to cho

ose in coordination games.

Maybe they get their gut feeling from Insula and ACC?

Coor-Domi

To solve a dominance solvable game requires a well defined number of steps. The greater is the nu

mber of steps, the more taxing might be the mental processes.

Maybe the fronto-parietal activation in dominance solvable games might correlate with the number of

steps?

Step

For coordination games, NCI (normalized coordination index) measures how well

coordination is achieved.

Choice1

Choice2

Choice1 Choice2 Choice1

Choice2

GroupA

10 0 5 5 10 0

GroupB

0 20 10 10 20 0

(1*0+0*1)*2=0

(0.5*0.5+0.5*0.5)*2=1

(1*1+0*0)*2=2

NCI 0 1 2

NCI

A high NCI means a high coordination rate, perhaps reflecting a strong gut feeling aroused by an obvious focal point while a low NCI (close to 1) means

choice is close to random.

Maybe the activation in insula and ACC in coordination games may correlate with the NCI?

NCI

We divide 40 dominance solvable games into 20 hard and 20 easy games depending on the number of steps and similarly divide 40 coordination games into 20 highly focal games and 20 less focal game

s.

We build a second model where the two kinds of games are modulated by the categories respectively

orSignal = bd[Domi] bdStep[Domi Hard or Easy]+bc[Coor]+bcFocal[Coor Focal or Less Focal] +bm[Motor]

+ε.

Step and NCI

Precuneus activates more in hard domi than in easy domi.

Precuneus plays a role in memory retrieval. The higher demand for memory imagery and retrieval in hard dominance solvable

games may explain this activation.

Insula activates more in highly focal coor than in less focal coor.

The participants may have felt quite strongly that the other must notice the same salient feature. This may be why insula activat

ion is higher for games which are more focal.

Step and NCI

A difficult game may generate a lower reward and different participants may disagree about which games are difficult.

We build still another model where each task is modulated by its grades,

Signal = bd[Domi] +bdgrade[DomigGrade] bc[Coor]+bcgrade[CoorGrade] +bm[Motor]+ε.

Payoff

Precuneus activation is negatively correlated with domi grades of a subject. Domi games with lower payoffs present harder mental challenges.

Insula activation is positively correlated with coor grades of a subject. Coor games with higher payoffs arouse the gut feeling stronger.

Payoff

The second and the third model suggest that the more “effortful” mental process activated by

dominance solvable games are more heavily taxed when the games are hard to solve, while the more

“effortless” mental processes activated by coordination games are more strongly activated

when coordination is easy.

This provides additional support for the main hypothesis of our research, that is, dominance solvable games and coordination games set off

two quite different mental processes.

Step, NCI, Payoff

The big question is, if we know that there are two very different networks that are activated when people play Domi or Coor games, can we apply what we have learned here to predict behaviors in other

games?

For instance, in trust games, do people reason or rely on intuition? Can we infer from the brain activations to make an educated guess at what they will

do?

Can we categorize players when they play an interesting game (like p-beauty contest) by their

brain data so that we know whether they are using a more calculating way or a more intuitive way to

reach their choices?

Hope you find the talk interesting.