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Summary of the paper
====================
This paper proposes a formal analysis of the "showrooming" phenomenon:
brick-and-mortar stores being used by consumers as a way to explore products
before buying them from online stores, effectively turning brick-and-mortar
stores into showrooms for online retailers. The authors model this phenomenon
as a competition between the brick-and-mortar retailer and the online retailer,
where the online retailer decides on a retail price while the brick-and-mortar
retailer decides on a retail price as well as a "sales effort". The competition
is then analyzed as Stackelberg game where either the online retailer or the
brick-and-mortar retailer moves first. In both cases, a closed-form expression
for the equilibrium is derived. The authors then proceed to a numerical
exploration of the equilibrium by plotting demand and profit for varying levels
of showrooming intensity and analyzing the optimal strategies of both retails
in multiple scenarios. Finally, an alternative strategy for the
brick-and-mortar retailer, opening an online store, is proposed and analyzed.
Novelty of the work
===================
As the authors mention in the related work section, very little research has
focused on theoretically analyzing showrooming. This paper does so by bringing
together two streams of literature: the first one studying competition between
retailers and the second one studying the impact of sales/promotional effort.
However, the following two papers do seem to propose a game theoretic analysis
of showrooming and while they do not seem to supersede the present work, they
should be mentioned in the related work section with a clear explanation of how
the present work differs from them.
1. Mehra, A and Kumar, S and Raju, J S (2012) Showrooming and the competition
between store and online retailers. In: 22nd Workshop on Information
Technologies and Systems, 15-16 December 2012, United States.
2. Chunhua Wu, Kangkang Wang and Ting Zhu, Can Price Matching Defeat
Showrooming? Manuscript, 2015
Discussion of the model
=======================
The situation is modeled as a fairly standard duopoly competition where both
retailers decide on a retail price. The original part is that the
brick-and-mortar retailer also decides on a sales effort, a fraction of which
contributes to increasing its own demand, while the remaining fraction
contributes to the demand of its competitor.
My main concerns regarding the model are the following:
* ultimately, showrooming is a property of the consumer: the consumer decides
to "free-ride" the brick-and-mortar store. It seems that a proper model for
showrooming should also consider the consumer to be part of the game (along
with both retailers) and modeled as a strategic agent deciding to free-ride
depending on the behaviors of both retailers.
* the showrooming parameter is exogenously determined. This seems to be
a severe limitation of the model and relates to the previous point. This
showrooming parameter is a coarse summary of the consumers' behavior which
should maybe be modeled explicitly. Furthermore, as shown in Figure 1a, the
main reason for showrooming are cheaper online prices, which indicates that
the showrooming intensity should also depend on the price difference between
the two retailers.
* the game is solved as a Stackelberg competition where one of the two
retailers moves first. But in the context described in the paper, it seems
that both retailers can be highly dynamic and keep adjusting their prices in
reaction to their competitor. It seems more appropriate to analyze this
situation as a repeated game between the two competitors.
Of lesser importance:
* a motivation/explanation of why the price elasticity can be considered
identical for both retailers would improve the exposition of the model.
* similarly for the specific choice of the square root function
to relate the sales effort to its contribution to demand. Would any other
concave function lead to the same results?
Theoretical results
===================
The Stackelberg equilibrium is computed in closed form by a standard
derivation. The different threshold functions defining the regions where each
retailer experience higher demand and profit are then derived from the
equilibrium in a straightforward manner. These results are correct as far as
I was able to verify.
Numerical analysis
==================
The numerical analysis section consists of plots of the closed-form expressions
obtained in the theoretical section. Since everything can be solved in
closed-form in this problem, and since most of the effects being shown are
quite intuitive and unsurprising, the length of this section does not seem
fully justified. I would maybe consider removing Figure 2 and merging Figure
3 and Figure 4 into one figure. This would put more emphasis on the one
counter-intuitive finding that high levels of showrooming do not benefit the
online retailer.
Strategic decision-making
=========================
Section 6 aims at providing managerial insights coming from the theoretical and
numerical results. However, a significant drawback is that the optimal strategy
strongly depends on the level of showrooming which is assumed exogenous in the
paper. This leaves the following question completely open: how as a retailer
can I determine which level of showrooming (and thus which cell of the array)
I am in? Without some indication that the level of showrooming could be
determined (for example estimated from data), the impact of the managerial
insights coming from this model is significantly lessened.
This section could also contain some analysis of real-life data: different
strategies followed by different retailers and which ones had a positive
impact. For example, the famous Bestbuy price-matching policy which has been
studied in the related literature could be analyzed in light of the theory
developed in this paper.
The meaning of the VL, L, H, VH strategies in table 2 and 3 should be
explained: how where the thresholds defining these different categories
determined?
Click-and-mortar model
======================
Section 7 is lacking some important details on how the results were obtained.
My understanding is that the authors solved for the Stackelberg equilibrium in
the new setting where the brick-and-mortar retailer nows sells via an extra
online channel. If this is the case it should be written clearly.
An alternative interpretation of this section could be that deciding to open an
online store is now a strategic action that can be taken by the
brick-and-mortar retailer, whether or not to take this action is part of the
description of the equilirium.
Without such an explanation, the reader cannot determined how Figure 6 was
obtained: what is the equation of the boundary between zone 1 and zone 2 in
each plot?
Comments on writing
===================
Apart from the specific comments on exposition given in the previous sections,
I found the paper very well written and easy to follow. Two minor typos
I found:
* page 6, first paragraph of section 2: interations --> interactions
* page 26 last paragraph, 3rd sentence: motor --> mortar
Conclusion
==========
While the problem of formally understanding showrooming is very interesting and
mostly unexplored by the current literature, the model adopted in this paper
suffers from questionable choices. The fact that the results are not confronted
to real world examples and depend on a key parameter (showrooming intensity)
which seems hard to determine also diminishes the impact of this work.
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