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Appendix A
The current model structure ( Figure 10 ) covers the following dimensions though subscripts :
Since every platform owner has to have an opinion of every platform , increasing the number of platforms on the market leads to the O ( avi 2 ) expansion of model state variables .
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It is important to maintain the integrity of stock levels , so that the same number of drivers has opinions about every existing platform .
Mathematically , it is represented as the following constraint
!,!
VV !,!,!,!
= VV !,!,!,! , kk , ll ∈ JJ , kk ≠ ll , JJ = aaaaaaaaaaaaaaaaaa pppppppppppppppppp , ∀ ii
!,!
The matrix M v , u is defined as
M !,! =
where the diagonal elements are equal to 0 , as the views cannot be changed to themselves . The last column is also 0 , as the model does not allow views to change to “ uninfluenced ” through the WOM mechanism since WOM implies influence ( favorable or unfavorable ).
0 |
pp !
|
0 |
pp !
|
0 |
0 |
pp !
|
pp !
|
0 |
Changes to uninfluenced are taken care of by the separate process of forgetting . Other elements p 1
- p 4 are the strengths of the transition between other combinations of views . Exact values depend on the market . In this model the following values are :
pp ! = pp !"#$%"&'( !" !"#$%&'$()* = 0.9 pp ! = pp !"#$%&'$()* !" !"#$%"&'( = 0.5 pp ! = pp !"#"$%!&"'&( !" !"#$%"&'( = 1 pp ! = pp !"#"$%!&"'&( !" !"#$%&'$()* = 1
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