Recipient of the Arrow Prize for Senior Economists

A BEJTE Advances article.

Abstract

We examine the spread of a disease or behavior through a social network. In particular, we analyze how infection rates depend on the distribution of degrees (numbers of links) among the nodes in the network. We introduce new techniques using first- and second order stochastic dominance relationships of the degree distribution in order to compare infection rates across different social networks.

Erratum

• Statement of Theorem 1 part (I) Page 6:
  
  Original:
  (I) If P' strictly first order stochastic dominates P, then ...
  Corrected:
  (I) If P' and P'(d)d/E_P'[d] strictly first order stochastic dominate P and P(d)d/E_P[d], respectively, then ...
• Last Sentence Before Corollary 2 on Page 8:
  
  Original:
  As a direct consequence of Theorems 1 and 2, we have the following.
  Corrected:
  As a consequence of Theorems 1 and 2 (noting that the proof of Theorem 2 from Jackson and Rogers [4] is easily extended to show stochastic dominance of the cumulative distribution function corresponding to f(d)d/m as m is increased by showing that the cdf is decreasing in m for all d > 0) we have the following.
• Sentence immediately following equation (5) on page 13:
  
  Original:
  ..., it follows from either strict first order stochastic dominance of P' over P, or that P' is a mean-preserving spread of P, that ...
  Corrected:
  ..., it follows from either strict first order stochastic dominance of P'(d)d/m' over P(d)d/m, or that P' is a mean-preserving spread of P, that ...

Submitted: November 2, 2006 · Accepted: December 7, 2006 · Published: February 22, 2007

Recommended Citation

Jackson, Matthew O. and Rogers, Brian W. (2007) "Relating Network Structure to Diffusion Properties through Stochastic Dominance," The B.E. Journal of Theoretical Economics: Vol. 7 : Iss. 1 (Advances), Article 6.
DOI: 10.2202/1935-1704.1341
Available at: http://www.bepress.com/bejte/vol7/iss1/art6