1. Risk aversion and networks Microfoundations for network formation
Jaromir Kovarik
University of the Basque Country
Marco van der Leij
University of Alicante
August 2009

2. Introduction
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:
How are social networks formed?
Why do some agents get into a good position and others not?
Two approaches:
Economic: Jackson & Wolinsky (1996)
Statistical Mechanics: Barabasi & Albert (1999)
Jackson (2006, 2008): Synergies possible!

3. Introduction
In this project, we first present a statistical mechanics model of network formation, in which:
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
Agents learn about the friends of friends
Search randomly if the friends of friends are all unattractive

4. Introduction
Our model allows us to make predictions on the role of risk aversion in the formation of social networks
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
Risk aversion is negatively related to payoff
Clustering is positively related to payoff

5. The Model The model is specified as follows:
Each period one agent i enters the network
network growth model
Agent i’s objective: to create m links maximizing utility
Benefit bij of i linking to j is initially unknown
bij is drawn from a i.i.d. distribution F with mean
We assume that agents have a CARA utility function

6. Link Formation

7. Link Formation
new node: i

8. Link Formation m l j k
new node: i

9. Link Formation m l j k
new node: i

10. Link Formation m n l j k
new node: i

11. Link Formation m n l j k
new node: i

12. Link Formation m n l j k
new node: i

13. Link Formation m n l j k
new node: i

14. Link Formation
new node

15. The Model
Our network formation model has the same network properties of Vázquez (2003) and Jackson & Rogers (2007)
Fat tail degree distribution
High clustering coefficient
Small network distances
Negative correlation Degree-Clustering
Positive correlation Degree-neighbor’s degree

16. Risk and network position
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?
Relation to in-degree, out-degree, degree
Relation to clustering

17. Risk and network position
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
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

18. Empirical Analysis
We test our predictions on a dataset of 256 undergraduate students at the University of Granada
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.

19. Network positions and payoffs
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
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.
Agents only link in network if benefit of neighbor is high enough

20. Summary We have presented a model of network formation
statistic model, which can be tested
microfoundations for decision to form a link
Risk aversion!
We relate risk aversion to network position
No relation risk aversion and degree
Positive relation risk aversion and clustering
These predictions are empirically confirmed

21. Conclusion
We obtain a negative relation between clustering and payoffs.
People with more clustered networks earn more.
This gives an alternative view to the standard sociological discussion on network position and payoff