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|
!"#$%"&
∆ !,!,!,!,! =
|
VV !,!,!,! M !,! PP !"#$%"& CCCCCC !
ττ !"#$%"&
, uu = ffffffffffffffffff
VV !,!,!,! M !,! ( − PP !"#$%"& CCCCCC ! )
, uu = uuuuuuuuuuuuuuuuuuuuuu ττ
!"#$%"&
|
vvvvhiiiiiiiiii yyyyyyyy |
, ∀ ii = jj |
where V i , j , v , a is a stock of vehicles , M v , u is the square matrix of allowed directions and strengths of view changes from view v to view u , P drivers is function of probability of view change given the customer satisfaction level CSL i
, and τ drivers is the time to change views of drivers of a platform in years .
Nondrivers form their opinions through the word of mouth by interacting with both drivers and other nondrivers of a technology platform .
!"!#$%&'$( !"#$
∆ !"#$%"& !,!,!,!,!
= VV !,!,!,! λλ M !,! PP !"#$%"& !,! ππ !"#$%"& vvvvhiiiiiiiiii yyyyyyyy
!"!#$%&'$( !"#$
∆ !"!#$%&'$( !,!,!,!,!
= VV !,!,!,! λλ M !,! PP !"!#$%&'$( !,! ππ !"!#$%&'$( vvvvhiiiiiiiiii yyyyyyyy
∆ !"# !"!#$%&'$( !"#$ !,!,!,!,! = ∆ !"#$%"& !"!#$%&'$( !"#$ !"!#$%&'$(
!,!,!,!,!
+ ∆ !,!,!,!,!
!"#$%"&
PP !,!
where λ is average contact rate , and
!"!#$%&'$(
PP !,! are probabilities of contact with drivers and nondrivers of technology j holding view v , and π drivers and π nondrivers are probabilities of view change after contact with drivers and nondrivers .
In addition , marketing provides the way to facilitate conversion of nondrivers to favorable category . The model assumes that drivers cannot be influenced by marketing efforts ; as they form their views based on the direct experience with the platform .
∆ !"!"#$%&' !,!,!,!,!
= VV !,!,!,! MM ! M !,! vvvvhiiiiiiiiii yyyyyyyy
, ∀ ii ≠ jj where M j is the total marketing effect for a platform j .
There is also a possibility that nondrivers will forget their opinion if not exposed to a platform for a certain period of time .
∆ !"#$%&&'($ !,!,!,!,!
=
VV !,!,!,! vvvvhiiiiiiiiii ττ
!"#$ !"#$%&&'($ yyyyyyyy
, ∀ ii ≠ jj , uu = uuuuiiiiiiiiiiiiiiii
Where τ view forgetting is time to forget the view in years . More detailed description of the model including explanations of other variables is in the Appendix A .
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