Risk aversion and networks
Microfoundations for network formation
Jaromir Kovarik
University of the Basque Country
Marco van der Leij
University of Alicante
August 2009
Introduction
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Many studies argue that individual economic
outcomes are for a part determined by the position
an individual occupies in the social network
This raises important questions on the formation of
social networks:
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How are social networks formed?
Why do some agents get into a good position and others
not?
Two approaches:
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Economic: Jackson & Wolinsky (1996)
Statistical Mechanics: Barabasi & Albert (1999)
Jackson (2006, 2008): Synergies possible!
Introduction
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In this project, we first present a statistical
mechanics model of network formation, in which:
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Agents enter sequentially, and search for partners
Random search and Local search (among friends of
friends)
 Vázquez (2003) and Jackson & Rogers (2007)
Decision to search randomly or locally is
endogenized and follows from utility-maximization
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Agents learn about the friends of friends
Search randomly if the friends of friends are all unattractive
Introduction
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Our model allows us to make predictions on the role
of risk aversion in the formation of social networks
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Risk aversion is not related to degree
Risk aversion is positively related to clustering
We empirically test and confirm these predictions
Our model allows us to relate individual payoffs to
individual network position
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Risk aversion is negatively related to payoff
Clustering is positively related to payoff
The Model
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The model is specified as follows:
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Each period one agent i enters the network
 network growth model
Agent i’s objective: to create m links maximizing utility
 
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U i ( g , b)  E ui   bij 
  jNi 
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Benefit bij of i linking to j is initially unknown
bij is drawn from a i.i.d. distribution F with mean b
We assume that agents have a CARA utility function
Link Formation
Link Formation
new node: i
Link Formation
m
l
j
k
new node: i
Link Formation
m
l
j
k
bik  b  ri  bil  bim
new node: i
Link Formation
m
n
l
j
k
bik  b  ri  bil  bim
new node: i
Link Formation
m
n
l
j
k
b  ri  bil  bin
new node: i
Link Formation
m
n
l
j
k
b  ri  bil  bin
new node: i
Link Formation
m
n
l
j
k
new node: i
Link Formation
new node
The Model
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Our network formation model has the same
network properties of Vázquez (2003) and
Jackson & Rogers (2007)
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Fat tail degree distribution
High clustering coefficient
Small network distances
Negative correlation Degree-Clustering
Positive correlation Degree-neighbor’s degree
Risk and network position
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Let the risk premium ri be i.i.d. from
distribution G
What is the relation of an agent’s risk
aversion to its network position?
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Relation to in-degree, out-degree, degree
Relation to clustering
Risk and network position
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Proposition: The agent’s risk premium ri is
uncorrelated with the agent’s number of links, di.
Number of links depends on the linking decisions of other
agents j entering after i
Proposition: The risk premium ri is positively correlated with the
clustering coefficient Ci
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The probability that an entering node i, after linking to j, decides
to link to a neighbor of j is increasing in ri
Everytime that agent i decides to link a friend of a friend, at least
1 edge between the neighbors of i is created
Everytime that agent i decides to link randomly, the probability of
a new edge between the neighbors of i is very small
Empirical Analysis
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We test our predictions on a dataset of 256
undergraduate students at the University of
Granada
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Dataset obtained through a series of lab experiments on
the same set of students in Spring 2005, see Brañas et al.
(2006, 2008)
We use data on two experiments:
 Network elicitation experiment
 Risk elicitation experiment
We test that risk aversion is not related to degree
and that it is positively related to clustering.
Both our predictions are empirically confirmed.
Network positions and payoffs
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Our model allows us to analyze the relation between
payoffs and network position
Proposition: The expected payoff of an agent with
risk premium r, is decreasing with r
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Risk averse agents accept a sure relative low payoff from
second-order neighbors in order to avoid risky decisions
Proposition: The expected payoff of an agent
conditional on her clustering coefficient, C, is
increasing in C.
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Agents only link in network if benefit of neighbor is high
enough
Summary
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We have presented a model of network
formation
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statistic model, which can be tested
microfoundations for decision to form a link
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We relate risk aversion to network position
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Risk aversion!
No relation risk aversion and degree
Positive relation risk aversion and clustering
These predictions are empirically confirmed
Conclusion
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We obtain a negative relation between
clustering and payoffs.
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People with more clustered networks earn more.
This gives an alternative view to the standard
sociological discussion on network position
and payoff