Biomedical Engineering Reference
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and computer science literatures that model networks as collections of connected
agents differentiated by their vulnerability (Dodds and Watts 2004 , 2005 ). For exam-
ple, the vulnerability of a physician i will be defined as the threshold number of con-
nected physicians that would have to take an action (therapy or dug adoption, increase/
decrease prescription of a particular drug) before physician i himself would succumb
to the action. The critical mass model was extended by Brock and Durlauf ( 2001 )
who cast the model in terms of discrete choice.
There are various approaches to modeling social interactions in economics
literature. The spatial models specify correlation structures such that responses by
individuals near one another generate similar outcomes. The measure for nearness
could be physical location (as in Manchanda et al. 2008 ), or attributes similar to
those used to prepare a perceptual map, or underlying preferences (as in patriotism
in Yang and Allenby 2003 ). A limitation of these models is that they cannot identify
whether an interaction is present. Another class of models in economics is that of
models with “forward-looking consumers.” These models set up repeated static
games where the consumer learns over time by interacting repeatedly in an uncer-
tain environment. For example, physicians learn over time by referring patients to
various physicians, which of those physicians are better than the others, or which
physicians are better for which kind of patients, and apply that knowledge in the
present when deciding who to refer the current patient to. Blume ( 1993 ) and Brock
and Durlauf ( 2001 , 2002 ) apply mean field theory to check expectations formed by
agents about group behavior, and the expectations are consistent with outcomes.
There have been economic models of the process of group formation (Bala and
Goyal 2000 ; Conley and Udry 2010 ). The network effects can work in either
direction. Most papers show positive effects, but some, such as the one authored by
Frank ( 1985 ), show negative social effects due to status-seeking. Show how net-
work externalities can actually slow diffusion of innovation. Stremersch et al.
( 2010 ) suggest that more work is needed on the separation of social contagion and
network effects.
There has been great interest in marketing in modeling social interactions.
The focus of this literature has changed over time from whether people's behavior
was affected by social interaction to who was affected, followed by why and how.
Some recent research models social contagion in a piano tuning service (Reingen
and Kernan 1986 ), student grade point averages (Sacerdote 2001 ), automobile
purchases (Yang and Allenby 2003 ), an internet grocer (Bell and Song 2007 ), and a
video-on-demand service (Nam et al. 2010 ). Godes and Mayzlin ( 2004 ) use field
studies to measure word-of-mouth effects from loyal and non-loyal customers of a
retail chain. They find that word-of-mouth seems more persuasive on “far” peers
rather than “close” peers. Also, surprisingly, word-of-mouth generated by non-loyal
customers is more effective than that generated by loyal customers. The Medical
Innovation Study (Coleman et al. 1966 ) in sociology was among the first to focus on
whether there are opinion leaders. The study was followed by Burt ( 1987 ) who used
more accurate identification, and Van den Bulte and Lilien ( 2001 ), who added mar-
keting variables to the model, while employing the data from the Medical Innovation
Study to better identify the social effects.
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