|A scientific approach to managing competition
|by Theodore Modis
Ever since the Belgian mathematician P. F. Verhulst formulated
the naturalgrowth equation to describe species populations back
in 1845, his ubiquitous S-shaped curve has made its way into everyday
life. Early in the 20th century, Alfred Lotka of Johns Hopkins University
and Vito Volterra of the University of Rome, working simultaneously
but independently, generalized Verhulsts growth equation to
model competition among different species. Today, the predatorprey
mathematical formulation bears both mens names, and its usefulness
has been extended to describe competition outside biology and ecology.
Indeed, the Volterra-Lotka model has opened the way to effectively
managing competition in the marketplace. A set of elementary marketing
actions has emerged that provide guidance when searching for a commercial
image or an effective advertising message.
An intriguing aspect of the marketplace is that the nature of competition
can change over time. A technology, company, or product does not
need to remain prey to another forever. Competitive roles can be
radically altered with technological advances or with the right
marketing decisions. External light meters, used for accurate diaphragm
and speed setting on photographic cameras, enjoyed a stable, symbiotic
(winwin) relationship with cameras for decades. As camera
sales grew, so did light-meter sales. But eventually, technological
developments enabled camera companies to incorporate light meters
into their own boxes. Soon, the whole light-meter industry became
prey to the camera industry. Sales of external light meters diminished
while sales of cameras enjoyed a boost, and the relationship passed
from winwin to predatorprey.
|Figure 1. Fountain
pen sales were following a classic S-shaped growth curve
when ballpoint pens were introduced in 1951. Fountain
pens counterattacked by undergoing a character displacement
and entering a luxury niche between 1951 and 1973, and
then they retreated into noncompetition.
||Battle of the
The struggle between fountain pens and ballpoint pens had a
different ending (Figure 1, left). The substitution of ballpoint
pens for fountain pens as writing instruments went through three
distinct stages. Before the appearance of ballpoint pens, fountainpen
sales grew undisturbed to fill the writing- instrument market.
They were following an S-shaped curve when the ballpoint technology
appeared in 1951. As ballpoint sales picked up, those of fountain
pens declined in the period 1951 to 1973. Fountain pens staged
a counterattack by radically dropping prices. But that effort
failed. Fountain pens kept losing market share and embarked
on an extinction course. By 1973, their average price had dropped
to as low as 72 cents, to no avail.
Eventually, however, the prices of fountain pens began rising.
The fountain pen underwent what Darwin would have described as a
character displacement to the luxury niche of the executive pen
market. In the early 1970s, the strategy of fountain pens became
a retreat into noncompetition. By 1988, the price of some fountain
pens in the United States had climbed to $400. The Volterra-Lotka
model indicates that today the two species no longer interact but
each follows a simple S-shaped growth pattern. As a consequence,
fountain pens have secured a healthy and profitable market niche.
Had they persisted in their competition with ballpoint pens, they
would have perished.
Character displacement is a classical way to diminish the impact
of competition. Another name for this is Darwinian divergence, sometimes
also encountered among siblings. In his book Born to Rebel: Birth
Order, Family Dynamics, and Creative Lives, Frank Sulloway shows
that throughout history, first-born children have become conservative
and later-borns revolutionaries. First-born children end up conservative
because they do not want to lose any of the only-child privileges
they enjoy. But this forces later-borns into becoming rebellious,
to differentiate themselves and thus minimize competition with a
sibling and optimize survival in the same family.
The attack of a new species against the defenses of an incumbent
one lies at the heart of corporate marketing strategies. Christopher
Farrell, director of scientific affairs at Baxter Healthcare Corp.
(Deerfield, IL), defined an attackers advantage and a defenders
counterattack in terms of the coupling parameters in the Volterrra-
Lotka model. A coupling parameter can be determined by data, and
thus, it can assign a precise number to an attackers advantage
or a defenders counterattack. The attackers advantage
quantifies the extent to which the attacker inhibits the ability
of the defender to keep market share.
Under attack, the defender redoubles its efforts to maintain
or improve its position. A high value for the defenders
counterattack implies a face-on counterattack within the context
what they do, we do better. Kristina Smitalova
and Stefan Sujan studied and classified the various coupling
schemes by which two competitors might interact. They distinguished
and labeled six ways in which two competitors can influence
each others growth rate, according to the sign of the
two coupling parameters (Table 1, right).
Pure competition occurs between rabbits and sheep. Each one
diminishes the growth of the other but not necessarily with
the same importance (sheep multiply more slowly but eat more).
Market examples are the competition among mobile-telephone
companies and among different-size computer models.
|Table 1. The six
ways that two competitors, A and B, can influence each
others growth rate can be summarized in terms of
positive, negative, and neutral coupling parameters, according
to Kristina Smitalova and Stefan Sujan.
An example of predatorprey interaction is the case of cinema
and television. The more movies made, the more television benefits;
but the more television grows in importance, the more cinema suffers.
Films made for TV are not shown in movie theaters. Without the legal
protection that restricts permission to broadcast new movies on
television, television would probably eat up the cinema audience.
A typical case of mutualism is software and hardware. Sales of
each trigger more sales for the other, as in the early relationship
between external light meters and cameras.
Add-ons and accessories such as vehicle extras illustrate commensalism.
The more automobiles sold, the more car accessories will be sold.
The inverse is not true, however; sales of accessories do not trigger
Amensalism can be found with ballpoint pens and fountain pens.
The onslaught of ballpoint sales seriously damaged fountain pen
sales, yet the ballpoint-pen population grew as if there were no
Neutralism arises in all situations in which there is no market
overlap, as happens between fountain pens and ballpoint pens today.
Another example is a sports store that sells both swimwear and skiwear.
Although sales of one may rise when sales of the other go down because
of seasonal variation, sales of one product do not generally affect
sales of the other.
The S-shaped pattern evidenced in the evolution of a species population
can in general be described with two parameters: one reflects the
ability of the species to multiply (or a products attractiveness),
and the other reflects the size of the ecological niche (or a products
market niche). But what happens if more than one species of competitor
is present? Besides rabbits and sheep, cows also eat grass. Worse
yet, what happens if there are also foxes on the range? Competition
between rabbits and sheep is not the same as between rabbits and
foxes. Faced with a finite amount of grass, sheep would probably
lament the rapid multiplication of rabbits, whereas foxes would
The main feature of the Volterra-Lotka equations is that they
can deal with how one competitor influences the growth rate of the
other. They do this by introducing a third parameter, the so-called
coupling parameter. Sheep and rabbits have a negative effect on
each others population because they reduce each others
food supply. In contrast, foxes damage rabbit populations, while
rabbits enhance fox populations. The coupling parameter reflects
how much one species affects anotherin other words, how many
sales you will lose or win because your competitor won one. The
magnitude of the parameter measures your ability to attack, counterattack,
|Table 2. Six basic
advertising strategies to increase prospects for growth
are defined by increasing or decreasing three parameters
for your product or your competitors productattractiveness,
niche size, and competition.
The Volterra-Lotka model has three parameters for each competitorone
reflecting the competitors ability to multiply, the second
the size of its niche, and the third the interference from the
other competitor. Thus, there are three lines of marketing action,
or six if we also consider the parameters of the other competitor
(Table 2, left). To increase our prospects for growth, we can
try to influence one or more of the following:
- the products attractiveness (increase ours or decrease
- the size of the market niche (increase ours or decrease theirs)
- the nature of the interaction (increase our attack or decrease
Each line of action affects one parameter at a time, but it is
not obvious which change will produce the greater effect at a given
time. It depends on the particular situation. The concrete actions
may include performance improvements, price changes, image transformation,
and advertising campaigns. Performance and price concern our
products only, but advertising with an appropriate message can in
principle influence all aspects of competition, producing an effect
on all six parameters. The question is how much of an effect a certain
effort will produce.
Some advertising messages have proven significantly more effective
than others. Success is not necessarily due to whim, chance, or
other after-the-fact explanations based on psychological or circumstantial
arguments. The roles and positions of the competitors determine
which advertising message will be most effective. Actual messages
are often elaborate, but in principle, all successful advertising
campaigns have exploited some combination of these six elements.
The effectiveness of advertising messages can be illustrated by
a classical competitive technological substitution, that of synthetic
fiber for natural fiber in the fabrication of carpets. For centuries,
carpets were woven on a loom for which wool was well suited. But
around the middle of the 20th century, a new tufting technique favored
long, continuous filaments. At the same time, synthetic fibers such
as nylon became available, and nylon-tufted carpets began replacing
Solving the Volterra-Lotka equations for the carpet-sales data
yields negative coupling constants for the two competitors, a typical
situation of pure competition of the rabbit-sheep type. But the
attackers advantage was greater than the defenders counterattack,
and so was its attractiveness. Therefore, the fate of the defender
was eventual extinction. Today, woven-wool carpets represent less
than 1% of carpet sales. Could the makers of woven-wool carpets
have secured a market niche the way fountain pens did? If so, what
line of action should have they adopted? We can go back to 1979
and play out six scenarios exploring alternative lines of advertisingchanging
the six parameters one at a time by the same amountto test
their results. It turns out that effective campaigns would have
been those that emphasized attractiveness and differentiation with
messages such as Wool is good and Wool is different
from nylon as opposed to a counterattack along the lines:
Wool is better than nylon. These conclusions could not
have been arrived at by intuitive or other methods traditionally
used by advertising agencies, and they could be completely different
at another time or in another market.
Of crucial importance, of course, is the amount of effort required
to achieve the targeted change. There is a way to estimate the size
of the advertising investment needed. An advertising campaign along
the line Our product is good affects the products
attractiveness just as a price cut does. The costs incurred from
price dropping can thus be compared to those of an advertising campaign
that achieves the same result. It should be noted, however, that
if the survival of woolen carpets depended on price dropping alone,
the price would have to be cut to zero.
The Volterra-Lotka model accounts for the three fundamental factors
that shape growth: the attractiveness of an offering, the size of
its market niche, and its interaction with the competitor. When
there is more than one competitor, the situation can be reduced
to two by considering the major competitor only or by grouping all
others together. Naturally, other factors influence growth, such
as sales channels, distribution, market fragmentation, total market
growth, market share, frequency of innovations, productivity, and
organizational and human resource issues. Many factors can be expressed
as combinations of the three fundamental ones. Alternatively, the
model could be elaborated to take more phenomena into account.
As it stands, the Volterra-Lotka model provides the baseline the
trend on top of which other, higher-order effects will be superimposed.
It guides strategists through effective manipulations of a competitors
roles in the marketplace. It should be used before any discussions
of investments, advertising tactics, or detailed planning take place.
The model works equally well for products, corporations, technologies,
and whole industries. Only the time frames differ. Strategists now
have a quantitative, science- based way to understand the crux of
the competitive dynamics and to anticipate the consequences of possible
A typical first question is, Should we differentiate or
counterattack? You can answer this question with a simulation
on a desktop computer using sales data and the Volterra-Lotka equations.
Just thinkat this very moment there may be a cost-effective
way to terminate the state of being prey to the voracious competitor
that has been feeding persistently on your achievements.
Farrell, C. Survival of the Fittest Technologies. New Scientist
1993, 137, 3539.
Foster, R. Innovation: The Attackers Advantage; Macmillan:
London, 1986; 316 pp.
Modis, T. Conquering Uncertainty; McGraw-Hill: New York, 1998;
Smitalova, K.; Sujan, S. A Mathematical Treatment of Dynamical
Models in Biological Science; Ellis Horwood: West Sussex, U.K.,
1991; 183 pp.
Sulloway, F. Born to Rebel: Birth Order, Family Dynamics, and
Creative Lives; Pantheon, Harvard University Press: Boston, 1996;
Physicist Theodore Modis
is founder of Growth Dynamics,
which specializes in strategic forecasting and management consulting
and is based in Geneva, Switzerland.