2004/8/3 Learning in a Netwrok Economy 1

Learning in a Network Economy

2004/8/3 Learning in a Netwrok Economy 2

A Simple Communication Network Model

Direct Contacts Natural evolution: Selection and Novelty Agent as a source of information concerning

beliefs Learning: adjust his own network and beliefs Evolving local networks and beliefs

2004/8/3 Learning in a Netwrok Economy 3

Overlapping Generation Economy A single perishable commodity A fixed supply of fiat money introduced by the

government in each period Two co-existing populations in the economy Individual agent lives for two periods with endowment

and 1W

2W

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Individual Agents Problem Solve

Subject to

)(),t(cln)t(cln)c,c(Umax itit

it

it)t(c),t(c it

it

1111 ++=++

)(),t(ww)t()t(c)t(c iiitit 21 21 +++

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Agents Network - I A source of valuable information i.e. his

belief about inflation Information on the beliefs of other

agents from his personal communication network consisting of many contacts

denote as kjC , or kjC < , enabling agent j to access agent ks information, but not vice versa

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Agents Network - II

denote agent j makes the dth contact with k

as d

kjC , , where )..0[ d jC as js own local network of agents.

}],,1[,1|{ , jkNkCkC kjj == , N: population size define jCN as js list of the numbers of thecontacts with every target agent in jC .

},0:{ jjkjkj CkddCN >=

2004/8/3 Learning in a Netwrok Economy 7

Agents Network - III

agent js list of all contacts at date t. ),......,( 1

jd

jj j

kkCS = , where

jj

s dsk ,......1, =

The ths contact of agent j is with jsk .

2004/8/3 Learning in a Netwrok Economy 8

A Graph of Network

a social network of agents, consisting of many local networks of agents, as COM.

]}..1[,{ NjCCOM j =

2004/8/3 Learning in a Netwrok Economy 9

Information Set jI = all information after all contacts

js dsk ......1, =

s.t. jCS and jkkCS ,

1= sj

sj

sj III

kjI , = all information from agent k

= sj

kk

Is

U=

sj

kk

dkj

dkj III

s

=

+= 1,,

Revenue Function

SCCSCS jjj = }||||{

SCCS j || represents a gain of providing information to othersSCCS j || measures the cost associated with contacting other

agents.

j represents agent js net revenue from contacts.

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2004/8/3 Learning in a Netwrok Economy 11

Individual Agents Problem

)1(ln)(ln),(max 1)1(),(

++=++

tctcccU itit

it

it

tctc itit

s.t.

iiii

tit twwttctc ++++ )()()1()( 21

Forecast Rule :

)()()]1([ tPtbtPF ii =+

Realised(t)

NgtStS

tPtPt

+=

+=

)1()(

)()1()(

2004/8/3 Learning in a Netwrok Economy 12

2004/8/3 Learning in a Netwrok Economy 13

Communication Strategy

Randomly initalise list of contacts and their frequency social contact sequenc (SCS)

= shuffled union of jCS s

= ( ]1,1[| Njkj

s

s: the ths contact of j is with sk )

Balance

)1()1(

,

,

==

= dkj

dkjt

j CifSampleCostCifSampleCost

Balanceinchange

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2004/8/3 Learning in a Netwrok Economy 15

Formation of a Belief

Average Rule Mode Rule GA Rule

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Genetic Belief

agents primitive belief before he begins to make any contacts

production of genetic belief mimics a process of inheritance from generation to generation

a socialising process, their ideas or thoughts may change based on the information from the socialising process

genetic belief of an individual agent is a result of the cumulative process of evolution of agentsbeliefs and is also part of it.

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Updating Network and Belief

Selection : by eliminating from the network the agents who have the least good information or beliefs available

Novelty: introduced in the network in the form of new contacts or new beliefs

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Structure of Simulation1. Randomly initialise the beliefs (genetic beliefs)

and contact lists of the first young generation andthe first old generation.

2. Members of the young generation make contactsaccording to their own contact lists i.e. the jCN . The sequence of contacts for members of the young generation follows the social contact sequence. Also. It is necessary to keep booking their balancesheets during the process of contacts.

2004/8/3 Learning in a Netwrok Economy 19

Structure of Simulation

3. The belief generating procedure follows theAverage rule, the Mode rule or the STGA rule

4. Calculate net communication revenue,consumption, saving and actual inflation

5. Update the communication strategies and geneticbeliefs for members of the old generation.

6. Check for convergence and stopping rules. If thereis no convergence and the stopping rules do notapply then return to 2, otherwise stop.

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Population SizeAverage Rule

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Population Size

Mode Rule

GA Rule

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Information contagion

A phenomenon of information aggregation (Vriend, 1999)

Information Feedback Following Majority Inherent features of the GA

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String length

Mode Rule

GA Rule

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Sampling cost

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Evolution of Beliefs

2004/8/3 Learning in a Netwrok Economy 26

Evolution of Population Holding Beliefs

2004/8/3 Learning in a Netwrok Economy 27

Evolution of Fitness

2004/8/3 Learning in a Netwrok Economy 28

Evolution of Beliefs

2004/8/3 Learning in a Netwrok Economy 29

Evolution of Population Holding Beliefs

2004/8/3 Learning in a Netwrok Economy 30

Evolution of Fitness

2004/8/3 Learning in a Netwrok Economy 31

Evolution of Social Network

2004/8/3 Learning in a Netwrok Economy 32

Evolution of Social Network

2004/8/3 Learning in a Netwrok Economy 33

Conclusion In most of the experiments, the low inflation rational expectation

equilibrium (LRE) of the model emerged. Consist with many previous studies. the high inflation equilibrium never emerges in all experiments

Exist many intermediaries and their roles efficiently solve the problem of division of information i.e. some common sources of the agents are present in the social network and therefore efficiently solve the problem of division of information

STGA rule under-performed, compared with the belief generating procedure based on the average rule or the mode rule

Social learning results in many local interactions and these interactions create social conformism

Learning in a Network EconomyA Simple Communication Network ModelOverlapping Generation EconomyIndividual Agents ProblemAgents Network - IAgents Network - IIAgents Network - IIIA Graph of NetworkInformation SetRevenue FunctionIndividual Agents ProblemRealised (t)Communication StrategyBalanceFormation of a BeliefGenetic BeliefUpdating Network and BeliefStructure of SimulationStructure of SimulationPopulation SizePopulation SizeInformation contagionString lengthSampling costEvolution of BeliefsEvolution of Population Holding BeliefsEvolution of FitnessEvolution of BeliefsEvolution of Population Holding BeliefsEvolution of FitnessEvolution of Social NetworkEvolution of Social NetworkConclusion