1

Equilibrium analysis ofthe distribution of information in human society

revisited in August, 2009

Shigeki Goto (Waseda University)

Hisao Nojima (Seijo University)

2

Friends are my treasures.

In Network Society, each individual lives

autonomously. Still, you are not alone.

Network maniac lonely life

is not a correct diagram.

The ICT Revolution is the second phase of the

Industrial Revolution.*) Information and Communication Tech.

3

Adam Smith and the Industrial Revolution

His famous book:“An inquiry into the nature andcauses of the wealth of nations”

The Industrial Revolution and transportation technology

Information and communication

4

Concept of division of labor

Mr. A has10 books

Ms. B has10 books

Lend and

Borrow

5

Mr. Aknowledge10

knowledge 10

1Total knowledge 60

cost10

cost 1

Mr. A

Total cost 15

Division of labor and others

1 1 1 110 10 10 10 10

6

Mr. Aknowledge 10

Knowledge 10

60Total knowledge

cost 10

10cost 10

Mr. A

60Total cost

When each individual lives alone

10 10 101010 10 10 10

7

brain

large society

brain

end users

Theory of overflow

8

2-layer

3-layer

Network society is not flat.

brain

gate keepers

9

Network society is not flat.

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Distribution of information

You do not have to be an expert in all the areas.

There is a social structure for division of labor.Investigation on the human memory (Wenger, 1987)

baseball cooking

A: baseball fan Good --

B: cooking expert -- Good

A & B Good Good

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When others would help you.

A case study T. Sakatani and H. Nojima,

The structure of information flow among network users, in Advances in Japanese Cognitive Science, Vol. 5, pp.49—71, 1992.

FindingsThere is a three-layer structure.The roles of gatekeepers (or brokers) are

important.

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Distribution of information Research scientists at NTT Laboratories

About 180 people Inquiry

145 scientist responded. The number of network users is 95.

Investigation Question-Asking behavior

ÅEÅEÅE

É\ÉtÉgÉEÉFÉAå§ãÜèä äÓëbå§ãÜèä

É\ÉtÉgÉEÉFÉAäJî°ïî

É\ÉtÉgÉEÉFÉAãZèpïî

èÓïÒâ»äwå§ãÜïî

ï®éøâ»äwå§ãÜïî

ç¼óøï®ê´å§ãÜïî

4### 1### 2### 3###

11##

1301 1302 1303 1304

12## 13##

å§ãÜïî

ÉOÉãÅ[Év

å¬êl

íŠçÇÃëŒè€(ïêë†ñÏínãÊ)

éøñ‚ǵǃǰÇÈêlÇÃêî

êlêî

êl40

35

30

25

20

15

10

5

00 1 2 3 4 5 6 7 8 9 10 11 12 13 15 19 28 31 32

How many people ask you?

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Three-layer structure

Brains

Gate-keepers

End Users

E11...E 1n

End Users

E21...E2n

End Users

E31...E3n

B1

B2

B3B4

B5

GK1 GK2 GK3 GK4 GK5

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Characteristics of the structure It is an informal structure. It does not follow the

structure of the company. Three groups of people

Brains: small number of people who have much knowledge Gate Keepers: small number of local experts who can

cover wide area of topics End Users: many people who have little knowledge

Each brain recognizes who are other brains. A brain has his/her specific field of knowledge. Each gatekeeper does not know who are other

gatekeepers. A gatekeeper does not have any specific area of

knowledge. He/she knows general information.

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Equilibrium analysis of the three-layer structure

S. Goto and H. Nojima,Equilibrium analysis of the distribution of information in human society,Artificial Intelligence, 75 (1995), pp.115—130.

H. Nojima,Cognitive Analysis on Roles of Others in Problem Solving,Ph.D Thesis, Waseda University, March, 2003.

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The three-layer structure is economically reasonable.

Brains

Gate-keepers

End Users

E11...E 1n

End Users

E21...E2n

End Users

E31...E3n

B1

B2

B3B4

B5

GK1 GK2 GK3 GK4 GK5

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Micro-ecomonics or Price theory

Knowledge as utilityEquilibrium of demand and supplyDemand — utility functionSupply — cost function

Two-layer structurea brain and end usersdivision of labor

Three-layer structureThe two-layer structure is not stable in a large society.

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Equilibrium point

Knowledge as utility ： utility function Zipf’s Law

Cost of knowledge: cost function Approximate the cost function based on computer

memory structure

At the equilibrium point, utility=cost. The equilibrium point is meaningful to a single person. He/she memorize a word, if utility > cost.

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Utility function — Zipf’s Law

%

1010

5

3.33

2.52

1.67 1.43 1.25 1.11 1

5

00 1 2 3 4 5 6 7 8 9 10

èáà 

10r

(%)

Occurrence of English words, Zipf (1949) 1st: the (10%) 2nd: of (5%) 3rd: and (3.3%) 4th: to (2.5%)

Empirical law which is applied to Population of cities Commands in Emacs Number of accesses to

popular WWW pages Use Zipf’s law as a diminishing

marginal utility function

å¿äEå¯óp

êîó 

Marginal utility function

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Equilibrium point

Knowledge as utility ： utility function Zipf’s Law

Cost of knowledge: cost function Approximate the cost function based on computer

memory structures

At the equilibrium point, utility=cost. The equilibrium point is meaningful to a single person. He/she memorize a word, if utility > cost.

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Cost function — memoryîÔóp

åXÇ ́b

åXÇ ́b

åXÇ ́b

a1

a2

a3

íPåÍÇÃêî

å¿äEîÔóp

b

a1

ÅEÅEÅE ÅEÅEÅE ÅEÅEÅE

a2a3

íPåÍÇÃêî123

Number of words

bcost b

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Equilibrium — a single user

b

å¿äEå¯óp

å¿äEîÔóp

utility = cost

Number of words

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Twp-layer structure

Which is better, live alone or depend on a brain? No division of labor if people live by themselves.

Division of labor means depending on others.

Cost analysis Social cost = Brain cost ＋ End User cost

When division of labor is meaningful?

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Equilibrium point of end users and a brain

k > 1(費用が効用を上回る)

k < 1(他者を頼る費用が効用より下)

A

BC

O: the original equilibrium pointX: depending on a brainA—B: keep memory by oneselfB—C: use the knowledge of a brain

higher cost

lower cost function

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Equilibrium point of a brain

re

brain

originalequilibrium point

end user

Start depending on a brain A brain has more knowledge.

Utility function of a brain

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From two-layer to three-layer

The two-layer model does not scale. The cost increases.

The links to the end users. Overflow theory

The end users should wait for a long time, and the cost for communications would increase.

The relay point — a gatekeeper

brains

end users

・・・

・・・

・・・

・・・

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Three-layer structure is found elsewhere

Popular structure in human society

Examples education WWW Server--client bibliography distribution

Brain teacher original WEB page

server Originalpaper

factory

Gate- Keeper

teaching assistant

cache server request manager textbook Wholesaledistributor

End User student browser client paper retailer

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Applications

Several issues are discussed from this point. How to make good successors of brains.

The difference in the amount of knowledge is huge between a brain and an end user.

It is economically sound to depend on brains. The issue is how to make good successors of brains.

How to solve the overflow. It is not necessary to have human gatekeepers. Manuals, dictionaries, textbooks are helpful to end

users.

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Conclusion

Three-layer structure ：

Knowledge is distributed.

The structure is economically reasonable.

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Lesson: division of labor The concept was well described by Adam Smith.

Transportation supports the industrial revolution. ICT will further promote the division of labor.

Many things are based on information.

Network society is not simply flat.Layered structures are stable in a large society.

Brain

Broker =Gate-keeper

End User