Biomedical Engineering Reference
In-Depth Information
Table 19.2 shows, the vast majority of response models, however, do not account for
competitive interaction. Among the few contributions that consider competitive
interaction is a model suggested by Shankar ( 1997 ). His model describes a duopoly
situation where the pioneer is challenged by a follower brand. Both firms may play
a Nash game or a Stackelberg leader-follower game in two spend categories, detail-
ing and advertising. Depending on the game, it is possible to predict the optimal
behavior of the pioneer in reaction to the entry of the new competitor. Application
of the model to a pharmaceutical category improved the prediction of the pioneer's
reaction behavior compared to alternative models.
Chintagunta and Desiraju ( 2005 ) extend Shankar's ( 1997 ) framework by allow-
ing a broader range of competitive interactions within the market. In addition, they
acknowledge that pharmaceutical firms often compete with each other in several
international markets. Following the theory of multimarket contact competition,
their model approach also includes across-market contact effects. Assuming a firm
wants to maximize profits Π jt for brand j in period t across all countries c where the
drug is marketed, the objective function is given by
(
)
1
C
c
c
c
P jt
=
pcQD
(19.2)
jt
jt
jt
jt
c
where p denotes price, c denotes marginal cost, Q is the demand for the brand, and
D is the level of detailing expenditures. The authors decompose brand demand into
a mixed logit share model and a category sales model that are estimated separately.
From ( 19.2 ), the first-order condition can be obtained:
=−
P jt
−=
(
)
(
)
K
C
J
c
cj
c
ck
z
zc
zk
pcQd
+
θ
Qd
+
pc Qd
jt
θ
10
(19.3)
z
zc
=
1
k
kj
=
1
k
kj
=
1
c
jt
jt
jt
kj
jt
jt
kj
jt
D
jt
Within-marketinteraction
Across-market contact effect
In the above equation, Qd j ck represents the first derivative of the sales of brand j
in country c with respect to the detailing level of brand k in that country. Under
conditions of competitive substitution, Qd j cj > 0 and Qd j ck < 0 . The term q k c is a
competitive interaction parameter that measures to what extent the firm deviates
from Nash behavior. If the firm plays Nash, q k c equals 1. For q k c > 0 interaction is
less competitive leading to lower detailing investments. The opposite is true for
q k c < 0 . In addition, across-market interactions may also be present. The interaction
parameter q k zc reflects the interaction between brands j and k across markets c and
z . For q k zc > 0 , as an example, contact in markets c and z results in more cooperative
behavior between brand j and k in market c .
Chintagunta and Desiraju ( 2005 ) take this model to data for a major drug cate-
gory in the USA and two European markets. They find both within-market and
across-market contact effects of competitive interaction. The effects are different
across brands and markets. For example, European markets seem to have no impact
on detailing levels in the USA, but the analysis reveals interaction effects in the
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