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ECON0123 Week 7
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Week 7Cascades and opinion dynamics, epidemics
EK Ch
Di usion of innovation
Why
• Informational e ects - indirect information is gathered from neighbours decisions, leading to a
change in your behaviour
• Direct-bene t e ects - you change your behaviour because a neighbours decision makes it
pro table
• Determinants of di usion
◦ Complexity of use and understanding of innovation
◦ Ease of observability
◦ Trial ability to mitigate adoption risks
◦ Compatibility with usage, expectations or values within the network
Modelling
B B ab o
Alaal10,01 U i'spairwiseinteractions
t10,0 bb
rule
Threshold
Ptofi's A
neighboursplay
1ptplayB
BR A
if Pdib
Cascading behaviour
• Cascading behaviour is how networks can shift between equilibria
◦ In each period, each node uses a threshold rule to decide whether to switch
◦ Assume sᵢ= A if A~B
• In the case some play A and some play B there is coexistence
a 3 b2 Sthreshold is p0.4
I Si B ti
a VandWadoptA
s tandr adoptA
sanduadoptA
Theset vw atthreshold 90.4
induces acompletecascade
, • Increasing the payo a from 3 to 4 means the
threshold drops from 0.4 to ⅓ and there is a
complete cascade
• If threshold cannot be changed (ie. your
technology cannot be improved), target the right
entry points
◦ After the rst round of switches, bringing 12
or 13 onboard su ce to win the bottom part
of the network
Clusters
A cluster of density p is a set of nodes such that each node has at least a fraction p of neighbours in
the set
Given a set of initial adopters for A, let q be the adoption threshold for A in the remaining network
• If the remaining network has a cluster of density > 1-q, there will not be a complete cascade
• If a set of initial adopters does not induce a complete cascade with threshold q, the remaining
network must contain a cluster of density greater than 1-q (only clusters stop cascades)
Di usion and weak ties
Awareness must precede adoption
• The strength of weak ties means that you are more likely to learn something new from weak ties,
as strong ties are likely similar to you
Individual thresholds
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