Learning in a Network Economy - aiecon.org file2004/8/3 Learning in a Netwrok Economy 2 A Simple...
Transcript of Learning in a Network Economy - aiecon.org file2004/8/3 Learning in a Netwrok Economy 2 A Simple...
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
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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 >=
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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 .
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A Graph of Network
a social network of agents, consisting of many local networks of agents, as COM.
]}..1[,{ NjCCOM j =
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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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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()(
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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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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.
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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
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Evolution of Population Holding Beliefs
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Evolution of Fitness
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Evolution of Beliefs
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Evolution of Population Holding Beliefs
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Evolution of Fitness
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Evolution of Social Network
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Evolution of Social Network
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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