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
port
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.