Advertising effectiveness and spillover:
simulating strategic interaction using
advertising
Malcolm P. Brady*
Malcom Brady is
a lecturer in
management in the
Business School
at Dublin City
University, Ireland,
where he has taught
courses in strategy,
process management,
and problem
structuring and
decision making. He
worked in industry
for many years before
entering academia in
1996. He obtained his
PhD in economics
from Lancaster
University
Management School
in 2005. His main
research interest is in
the modeling of
strategic interaction
among fi rms. He has
a second research
interest in business
process modeling.
Abstract
This paper reports on a model of advertising-driven competition based on the Cournot analytical
duopoly model using a system dynamics approach. The paper discusses the feedback loops that are
derived from the analytical equations and shows simulation results for a number of competitive
scenarios. The paper identifies and discusses three different inter-firm feedback loops. The scenarios
demonstrate that small changes in model parameter values can lead to significant differences in
firm and industry behaviour; a bifurcation in duopoly behaviour at low and high levels of advertising effectiveness is demonstrated. The simulation model demonstrates that positive spillover
(cooperation) reduces the impact of advertising and supports the free-rider hypothesis where
advertising is cooperative. The model also demonstrates that negative spillover (predation)
increases the impact of advertising when both fi rms advertise. The paper proposes simulation as
an alternative to the differential game approach when studying dynamic economic systems.
Copyright © 2009 John Wiley & Sons, Ltd.
Syst. Dyn. Rev. 25, 281–307, (2009)
Introduction
Advertising is all-pervasive in the modern world and industry spends billions
of dollars annually on product advertising. Effective use of advertising is of
enormous consequence for fi rms and is an active topic of research for scholars
in economics, marketing and management. This paper describes a simulation
model of inter-firm competition where advertising is used by fi rms as a competitive weapon. The paper demonstrates that a fi rm that is more effective
at advertising gains a strategic advantage over its less effective rival. The paper
also demonstrates that a bifurcation occurs in industry behaviour: at levels
of advertising effectiveness below a threshold level little advertising occurs
and the industry does not grow; at levels of advertising effectiveness above
a threshold level a substantial amount of advertising is selected by firms and
the industry grows exponentially. The paper also examines the issue of advertising spillover—when advertising by one firm has an impact on demand for a
rival fi rm’s product. Advertising is cooperative when advertising of one firm
increases the demand for its own product and also that of its rival. Advertising
is predatory when advertising by one fi rm increases demand for its own product but reduces demand for its rival’s product. The model demonstrates that
* Correspondence to: Malcolm P. Brady, Business School, Dublin City University, Dublin 9, Ireland. E-mail:
[email protected]
Received September 2007; Accepted March 2009
System Dynamics Review Vol. 25, No. 4, (October–December 2009): 281–307
Published online 11 November 2009 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/sdr.426
Copyright © 2009 John Wiley & Sons, Ltd
281
282 System Dynamics Review Volume 25 Number 4 2009
both fi rms are better off when advertising is predatory and both are less well off
when advertising is cooperative.
The simulation model is based on the Cournot analytical model of duopoly,
which is now the dominant paradigm in the field of industrial organisation
economics (Martin, 2002). The basic Cournot duopoly model (Dixit, 1979;
Perloff, 2008, pp. 453–464) leads to an equilibrium which can be determined
analytically. However, the model is essentially static: the equilibrium so determined will remain for all time unless conditions change. This paper extends
the basic Cournot model in two ways: firstly, from a static to a dynamic model
using simulation as a means of viewing the evolution of the Cournot equilibrium over time and, secondly, to include advertising. These two extensions
are interrelated: advertising causes industry demand conditions to change over
time, and the simulation model allows the resulting evolution of the Cournot
equilibrium to be observed. I adopt the explicit advertising function suggested
by Friedman (1983), which shifts the demand function for the fi rm to the right.
This occurs for both fi rms and so industry competitive conditions alter and a
new Cournot equilibrium will be determined. I allow two parameters in the
model to vary: advertising effectiveness and advertising interaction (spillover).
Different dynamic industry behaviour arises depending on the combination
of the values of these two parameters. This behaviour is not evident from the
static model: it is not possible to tell from the static Cournot model whether
the industry grows or stagnates or whether one firm dominates the other in the
long run. The simulation model demonstrates all these behaviours under
different conditions of advertising effectiveness and spillover.
The modelling approach is different from that of many system dynamic
papers in a number of ways. Firstly, the model is built up from a set of
equations derived from formal theory rather than built from constructs derived
from empirical observations. Secondly, the model dynamics are not stimulated by shocking the system in some fashion, e.g. by use of a step or pulse
function, but are inherent in the system of equations. Thirdly, the purpose of
the model is not to determine whether the system comes back to equilibrium
after such a shock but simply to determine the pattern of fi rm behaviour that
arises under different initial conditions; indeed, as will be shown, the system
often does not come to a long-term equilibrium. The model, however, is still
very much a dynamical system and the purpose of the simulation is to determine the system dynamic behaviour under a number of different fi rm policy
conditions.
The paper is organised as follows. Firstly, I briefly review the literature on
advertising, advertising models and the literature on system dynamics simulation of strategic interaction and advertising. Secondly I describe the analytical
model in detail, and thirdly I describe the simulation model. Then I discuss the
results of the model for a number of specific scenarios that examine advertising
effectiveness and spillover. Finally, I conclude and suggest some avenues for
future research.
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(www.interscience.wiley.com) DOI: 10.1002/sdr
M. P. Brady: Advertising Effectiveness and Spillover 283
Advertising
Chamberlain (1933, p. 72) suggests that advertising is one of three policy
variables that fi rms have at their disposal with which to maximise their profits,
the other two being price and product. He suggests that use of advertising
allows the fi rm to make two kinds of gain. Firstly, by providing information
about the product potential buyers know in advance that the product exists
and how well it will meet their needs; buyer uncertainty is thus reduced and
more buyers may purchase the fi rm’s product. Secondly, by altering wants
of consumers through advertising, fi rms may persuade more consumers to
purchase their product. Kaldor (1950) suggests that the distinction between
informative advertising and persuasive advertising is one of degree rather
than kind: “all advertising is persuasive in intention (i.e. it is supplied with
a view to fi nding prospective buyers), and is informative in character (in the
sense that it supplies some information, even if it is only the name of some
fi rm or product)”. This dual function of advertising as a source of information
and as a means of persuasion still forms the basis for much of the discussion of
advertising in the literature.
Nelson examined the role of advertising as a source of information about
price and quality of goods. He suggests that consumers gain information about
goods in two ways: by search, thereby gaining information about price and
possibly about quality, and by experience, i.e., by purchase and use of the
goods, thereby gaining definitive information about product quality (Nelson,
1970). He suggests that information on quality is more difficult and more
expensive to obtain than information on price. Nelson (1974) suggests that
advertising should give direct information about search goods but in the case
of experience goods “the most important information conveyed by advertising
is simply that the brand advertises”. Consumers expect very little information
from advertising for experience goods and will base their decision on the volume
of advertising carried out, taking this as a proxy measure for the quality of the
good. Nelson hypothesises that “producers of experience goods will advertise
more than producers of search goods” and that “advertising of experience
qualities increases sales through increasing the reputability of the seller, while
advertising of search qualities increases sales by providing the consumer with
‘hard’ information about the seller’s products”. While Nelson’s work gives
considerable insight into the rationale for advertising, the way advertising
affects consumer behaviour, and how consumer behaviour impacts on advertising, he views advertising largely as a signalling process.
A number of researchers have examined the economic value of advertising.
Borden (1947) found the economic impact of advertising to be positive. He
concluded that advertising stimulates demand, which allows fi rms to gain
economies of scale and reduce production costs. This increased demand attracts
in new entrants who have lower costs because they do not need to advertise
and so can charge lower prices in order to gain market share. Firms that
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284 System Dynamics Review Volume 25 Number 4 2009
advertise are therefore forced to reduce prices, passing on the reduction in
production cost to consumers. This reduction in prices has the secondary
effect of allowing fi rms to exploit elasticity of demand, which they may be
fearful of doing of their own accord. His view is that advertising is a cost of
growth but one which leads to greater social welfare: a greater amount and
variety of goods available at lower prices than before. Kaldor (1950) came to
a different conclusion: he found that “the cost of providing this highly
inadequate and defective information-service is exorbitantly high”. However,
he did concede that advertising played an instrumental role in the breaking
by manufacturers of the wholesalers’ stranglehold over industry in the early
part of the 20th century and that this resulted in greater production efficiency.
Telser (1964) considered the issue of whether or not advertising mitigated
against competition. Telser regarded advertising as “an input supplied together
with the product” and identified five functions carried out by advertising: it
provided information about the product; it signalled the quality of the product;
it identified sellers; it may be an integral part of the product; and it may
provide entertainment, for example, through sponsorship. He noted that the
received wisdom at the time of his writing was that advertising was believed to
be closely correlated with monopoly power: fi rms with monopoly power were
most likely to advertise as they received a significant portion of the gains from
their advertising; or, alternatively, advertising led directly to monopoly power
by differentiating the product of the fi rm from its competitors. Telser carried
out three different analyses of empirical data and concluded that advertising
did not reduce competition; indeed, by motivating new entrants it fostered
competition.
The above discussion centres on the nature and value of advertising. Other
researchers have developed formal models of advertising: advertising as a
signalling mechanism for product quality, as a combat tool for increasing
market share, as a mechanism for increasing sales, and as a means of influencing
strategic interaction. Dynamic models have been developed using a differential
game theoretic approach or, as in this paper, a simulation approach. Among
those researchers who use a simulation approach are system dynamicists.
I now briefly review formal models of advertising.
Advertising models
Several authors have put forward models of advertising as a mechanism for
signalling the quality of the product. Milgrom and Roberts (1986) consider
price as well as advertising as a means of signalling product quality of newly
introduced experience goods and recast Nelson’s work as a game theoretic
model. They conclude that the primary signal of product quality is given by
price, advertising being used only when insufficient differentiation is generated by the price signal. Schmalensee (1978) also puts Nelson’s ideas into
Published online in Wiley InterScience
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M. P. Brady: Advertising Effectiveness and Spillover 285
mathematical form. In his model the amount of advertising acts as a signal for
the product quality of experience goods; the model allocates market share to
fi rms in proportion to their advertising expenditure and consumer perception
of their product quality. Bagwell and Ramey (1994) examine the mechanism
by which advertising improves coordination between buyer and seller and
leads to mutual benefit by avoiding market failure (which they defi ne to be
either efficient fi rms being unable to obtain market share or market splitting
resulting in firms unable to gain full economies of scale). They view advertising
as a signal of price and, using a two-stage game theoretic approach, conclude
that advertising is necessary to ensure market coordination, especially when
consumers have no other means of inferring fi rm efficiency.
A number of researchers have developed models of advertising based on
Lanchester’s combat model (Kimball, 1957; Little, 1979). This model has its
origins in warfare and likens the marketplace to a combat situation. It assumes
that change in a fi rm’s market share is increased in proportion to its effectiveness in winning over a rival’s customers and decreased in proportion to a
rival’s effectiveness in winning over its customers. Lanchester’s models assume that fi rms persuade customers loyal to the rival fi rm to purchase the
fi rm’s product and the rate of change of fi rm market share is proportional to
the amount and effectiveness of advertising and the size of the rival’s market;
the rival also advertises in a similar fashion. Signalling and combat models
use advertising as a mechanism for allocating market share, not as a mechanism for increasing the size of the market. I now turn to a set of models that
view advertising as a force to increase the size of the market.
Vidale and Wolfe (1957) suggest a formal model where the sales response to
advertising takes into account market build-up, saturation and decay. Their
model suggests an S-shaped sales response to advertising similar to the wellknown product life cycle curve. Deal (1979) extends the Vidale–Wolfe model
to include competition: he puts forward a duopoly model where the sales
opportunity is determined as the saturation sales level less the combined
current sales of both fi rms. Mesak and Zhang (2001) extend the Vidale–Wolfe
model to examine optimal advertising pulsation policies (intermittent rather
than continuous time advertising) and also use a nonlinear function to model
sales response to advertising. Sasieni (1971) developed a model similar to that
of Vidale–Wolfe that also views rate of change of sales revenue as a function
of sales revenue, advertising and time. Neither the Sasieni nor Vidale–Wolfe
models take price into account.
Economists typically centre their models on the price/demand function.
The world view here is not that consumers are de facto loyal to any particular
product but that an increasing quantity will be purchased as price reduces
and vice versa. Nerlove and Arrow (1962) introduce the concept of a stock of
goodwill to model the cumulative effect of advertising. Their model assumes
that advertising influences demand in the current period but also continues to
influence demand in future periods, albeit in an ever-diminishing fashion.
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286 System Dynamics Review Volume 25 Number 4 2009
Advertising builds up a stock of goodwill, similar to a stock of capital, which
is used to produce revenue for the fi rm in future periods. Fershtman (1984)
extends the Nerlove–Arrow model from a single firm to a duopoly. Lambin
(1976, p. 28) represents the Nerlove–Arrow model in discrete time as a distributed lag structure with geometrically declining weights: goodwill in any
period is equal to advertising carried out in that period plus depreciated goodwill from the previous period.
Dorfman and Steiner (1954) use a microeconomic approach in developing
their theory of optimal advertising and take both price and quantity into
account. They show that for maximum profit the marginal value product
of advertising equals the price elasticity of demand. Bester and Petrakis (1995)
put forward a Hotelling model that considers both price and advertising.
Schmalensee (1976) adopts the Cournot behavioural assumption in a model of
promotional competition. Friedman’s (1983) goodwill model uses an explicit
linear demand function similar to that of Bowley (1924). He gives two guidelines for advertising models: fi rstly that they should recognise that the impact
of advertising is “cumulative rather than momentary”; and secondly that interfi rm effects exist. He suggests that inter-fi rm effects range along a continuum:
at one extreme advertising is highly cooperative, with rivals benefiting as
much from advertising as the fi rm that advertises, and at the other extreme
advertising is predatory, with fi rms benefiting strictly at the expense of their
rivals.
A more recent development is the use of optimal control theory (Seierstad
and Sydsaeter, 1987; Kamien and Schwartz, 1991) to determine the optimal
amount of advertising that a fi rm should select over time in order to ensure
long-run profit maximisation (Sethi, 1977; Feichtinger et al., 1994). The extension of the optimal control approach from the single firm to duopoly requires
use of the theory of differential games (Kamien and Schwartz, 1991, Ch. 23).
Many of the static advertising models discussed above have been extended to
differential games: Deal (1979) extends the Vidale–Wolfe model; Chintagunta
and Vilcassim (1992), Erickson (1992), Fruchter and Kalish (1997), Jarrar et al.
(2004) and Bass et al. (2005) extend the Lanchester model. Piga (1998) examines
advertising in a Hotelling-type differentiated duopoly as a differential game.
Piga (2000) extends Fershtman and Kamien’s (1987) “sticky prices” differential game model to include advertising. Cellini and Lambertini (2003) suggest
a Cournot model where advertising increases reservation price and solve this as
a differential game.
Differential games, especially the closed-loop (feedback) differential games,
require the solution of partial differential equations and are notoriously difficult to solve. Authors are usually forced to make a number of simplifying
assumptions (for example, that fi rms are symmetric or that the discount factor
is zero) in order to make the problem tractable. Wang and Wu (2007) demonstrate that one of these commonly used simplifying assumptions, that change
in market share is a function of the square root of advertising, is not supported
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M. P. Brady: Advertising Effectiveness and Spillover 287
by empirical evidence. Some authors have used numerical algorithms to solve
differential games (Wang and Wu, 2001).
Simulation has emerged as an acceptable method of research into business
and managerial problems (Davis et al., 2007) and is an alternative method
to differential games for examining the dynamic behaviour of two fi rms in a
duopoly. Relatively little work has been carried out to date using simulation
methods to examine inter-firm competition using advertising. This paper takes
a continuous time simulation approach to examining the behaviour of two
fi rms that use both advertising and price as competitive weapons. The paper
provides an alternative to the differential game approach to advertising
and Cournot competition taken by Cellini and Lambertini (2003); this paper
examines predatory as well as cooperative advertising, whereas Cellini and
Lambertini examine cooperative advertising only. The simulation approach
also has a number of advantages over the Lanchester differential game approach:
fi rstly, the total market size is allowed to grow in contrast to the Lanchester
model where it is held constant (market shares are allowed to fluctuate, but not
market size); secondly, it takes both price and advertising into account whereas
the Lanchester differential game either does not take price into account or, if it
does, as in Bass et al. (2005), requires an additional construct—a function to
allocate market share in addition to a function that allocates price according
to demand. Finally, the simulation model does not require the usual simplifying assumptions necessary to achieve a closed-form solution to a differential
game: for example, the requirement that fi rms be symmetric.
I will now briefly review the work of system dynamics simulation-based
researchers in the area of fi rm interaction and advertising.
System dynamics, firm interaction and advertising
System dynamicists have applied their research approach to the topic of
competitive interaction among fi rms and also to advertising, but rarely to both
elements together. A number of researchers have applied the system dynamics
approach to economic modelling. Radzicki and Sterman (1994) examine
duopoly using an approach that combines system dynamics, evolutionary
economics and the learning effect. Forrester (2003) discusses system dynamics
modelling of economic systems. Sice et al. (2000) consider a fi rst mover (von
Stackelberg) duopoly model that examines competitive interaction based on
product quality and demonstrates oscillating industry leadership and limit
cycle or chaotic industry behaviour. Sterman et al. (2007) use an approach that
combines duopoly theory with the behavioural theory of the fi rm.
System dynamicists have also applied their research approach to the issue
of fi rm advertising. Forrester (1959) discusses advertising policy and its correspondence to the product life cycle, arguing that advertising may merely
provide a mechanism for “borrowing” sales from the future. Forrester (2003)
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288 System Dynamics Review Volume 25 Number 4 2009
briefly discusses the dynamics of an advertising campaign. Graham and Ariza
(2003) present a model that optimizes allocation of fi rm advertising expenditure using a simulated annealing approach. Milling (1996, 2002) suggests an
innovation diffusion model of market growth and compares fi rm performance
under a number of different pricing policies. Advertising between competing
firms is an underdeveloped area in the field of system dynamics and this paper
aims to contribute to this area.
Kunc and Morecroft (2007) point out that system dynamics models rarely
attempt to model competition between fi rms, focusing instead on aggregate
industry or individual fi rm models. A contribution of this paper is to focus
specifically on inter-fi rm competition and examine the behaviour of each
individual fi rm under advertising, not fi rms in the aggregate. I now go on to
detail the analytical model and the simulation model.
The analytical model
Profit is the ultimate measure of fi rm performance and so I start with the profit
function of fi rm i, which is determined from the accounting identity:
Π i = pi qi − ci qi
(1)
where p represents unit price, q represents quantity sold and c represents unit
variable cost; subscript i refers to fi rm one or two in the duopoly. The fi rm
is assumed to be in control of its costs. A simple linear cost function is used
in Eq. 1 as more complex cost functions significantly increase the complexity
of the algebra when determining the Nash equilibrium quantities. Fixed costs
are assumed to be zero.
The market is assumed to determine price and quantity according to the
analytical model based on the work of Cournot (1838), Bowley (1924) and Dixit
(1979), whose work is founded on neoclassical economic principles. They
suggest that price can be modelled as a downward sloping function of quantity
placed on the market by both fi rms. For fi rm one in the duopoly this can be
expressed as
p1 = a1 − b1q1 − d1q2
and for fi rm two as
p2 = a2 − b2q2 − d2q1
where p is price, a is the reservation price, b is the own-price effect, d is the
cross-price effect and q is quantity placed on the market. For convenience I
adopt the commonly used i,j convention to represent equations for both fi rms
as one expression:
pi = ai − bi qi − di q j
i = 1, 2; j = 3 − i
(2)
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M. P. Brady: Advertising Effectiveness and Spillover 289
where subscript i refers to one of the two fi rms in the duopoly and subscript
j refers to its rival; for ease of exposition I leave out the sub-expressions i = 1,
2 and i = 1, 2; j = 3 − i in the remainder of the paper but they are understood.
The reservation price can be imagined as the highest price that is likely to be
paid for the good. The own-price effect represents the impact on price of placing
additional goods on the market. The cross-price effect represents the impact on
the fi rm’s price when its rival places additional goods on the market. The ratio
of cross-price effect to own-price effect represents the level of differentiation
between the two products: a value of one implies that the products are perfect
substitutes; a value of zero implies that the products are entirely differentiated,
each product being in effect a monopoly; a value of between zero and one
represents the level of product differentiation.
The model is in the Cournot (1838) tradition in that price is represented as
a function of quantity; i.e., fi rms are assumed to put a certain quantity onto the
market and the marketplace then determines a price for the good (the inverse
situation where a firm sets price and the marketplace determines quantity sold
is known as Bertrand (1883) competition). The Cournot approach is to determine the Nash (1951) equilibrium quantities for the two-fi rm competitive
situation: the equilibrium represents a pair of quantities such that neither firm
has an incentive to shift from their choice of quantity, given the choice made
by the other fi rm. This is achieved by differentiating the profit function (1)
of each fi rm with respect to own-fi rm quantity, setting the result to zero to
determine a maximum, and solving the two resulting equations (usually
referred to as “reaction functions”) simultaneously to determine the two Nash
equilibrium quantities. This process results in the following formal expression
of the Nash equilibrium quantities when products are differentiated:
qi =
2bj (ai − ci ) − di (a j − c j )
4bi bj − did j
(3)
Price is then determined from Eq. 2 above and profit in turn from Eq. 1. Eqs 1, 2
and 3 set up the market behaviour of the two firms and give the resulting profits
for the two fi rms.
Perloff (2008, p. 462) gives an explicit version of Eq. 2 for the microprocessor
industry:
p1 = 197 − 15.1q1 − 0.3q2
p2 = 490 − 10q2 − 6q1
where price is in dollars per microprocessor units, quantity is in millions
of units, subscript 1 refers to AMD and subscript 2 to Intel, and each fi rm faces
a constant marginal cost of $40 per unit. Note that the two firms are asymmetrically differentiated: Intel’s reservation price is much higher than AMD’s but
is also much more strongly influenced by the quantity that AMD brings to
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290 System Dynamics Review Volume 25 Number 4 2009
Fig. 1. Quantity
demanded at Nash
equilibrium for AMD
(1) and INTEL (2)
market, and vice versa for AMD. Perloff solves this system to determine equilibrium quantities and prices for the two differentiated fi rms to be 21 million
units at a unit price of $250 for Intel and 5 million units at a unit price of $115
for AMD. The equilibrium quantity figures can be confi rmed by substituting
the relevant values into Eq. 3 and prices confi rmed by substituting the results
into Eq. 2. The simulation model also confirmed these results as shown
in Figure 1, where the Cournot quantities are shown as two horizontal lines,
one for each fi rm; as this industry scenario is static the Cournot equilibrium
quantities remain constant for the two fi rms for all time.
The model as developed so far is static in that the equilibrium values determined according to the process outlined above will pertain for all time. I now
introduce advertising, Chamberlain’s third policy variable, into the model.
This brings a dynamic element to the model as advertising alters the demand
function for each fi rm, thereby changing the market conditions in which the
two fi rms compete. In each period the fi rms choose the amount of advertising
they wish to carry out, which in turn changes the demand conditions facing
the two fi rms. This change in competitive conditions yields a new Cournot
equilibrium. Therefore, over time, by changing the demand, and consequently
the competitive conditions, advertising continuously alters the market equilibrium. The simulation model provides a means of observing the evolution of
the Cournot equilibrium over time.
Introducing advertising has three distinct impacts on the model: fi rstly, the
effect of advertising on demand must be determined; secondly, the amount of
advertising selected by each fi rm must be determined; and thirdly, the cost of
advertising must be included in the model. I now discuss these three impacts.
The effect of advertising is to stimulate demand (Borden, 1947, p. xxix).
Specifically, advertising alters the demand function by shifting it outwards to
the right, which can be broadly regarded as increasing demand for the fi rm’s
product (Perloff, 2008, p. 433). In modelling terms such a shift means that
advertising increases the value of the reservation price, a. I follow Friedman’s
(1983) two suggestions: that the impact of advertising is cumulative and that
inter-fi rm effects exist. The cumulative impact of advertising is taken into
Published online in Wiley InterScience
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M. P. Brady: Advertising Effectiveness and Spillover 291
account in that once the demand curve shifts to the right it stays shifted and
does not revert to its original position. The inter-fi rm aspect of advertising is
modelled by including a spillover effect; i.e., advertising by one fi rm may also
increase demand for its rival’s product. I adapt Friedman’s (1983) expression
to determine the impact of advertising:
∆ai = ϕ i Ai + ρϕ j Aj
(4)
where a is the reservation price (the intercept of the inverse demand function
with the vertical axis), A is the amount of advertising, j represents the effectiveness of fi rm advertising and r is the advertising interaction parameter
representing the impact of rival advertising on the fi rm’s demand (spillover).
Therefore ∆a represents the change in demand due to advertising carried out
by both fi rms. In system dynamics terms Eq. 4 becomes a flow equation that
determines the rate of change of the stock variable a due to advertising. Note
that the advertising interaction parameter can be negative or positive—if negative,
then advertising by one fi rm reduces demand for the other fi rm’s product; if
positive, then advertising by one fi rm increases demand for the other fi rm’s
product. When the advertising interaction parameter is negative advertising
spillover is termed predatory, and when positive the spillover is termed cooperative. The advertising interaction parameter can also take a zero value; in
this case advertising by one fi rm has no impact on the inverse demand function of its rival. This does not mean that zero spillover advertising by a fi rm
will have no impact on its rival—it will, through the Cournot equilibrium
expression given in (3) above; fi rm advertising will increase fi rm reservation
price a and this will lead to an increase in the equilibrium quantity selected by
the fi rm and a reduction in the equilibrium quantity selected by its rival.
To determine the optimal amount of advertising for a fi rm I use Ferguson
et al.’s (1993) representation of the Dorfman–Steiner (1954) condition: optimal
advertising is a proportion of revenue in the ratio of advertising elasticity of
demand to price elasticity of demand:
Ai = Ri
ηAi
ηi
(5)
where revenue R is equal to price times quantity. Selecting advertising as a
proportion of sales revenue is a rule of thumb commonly used by managers
(Davis et al., 1991) and Eq. 5 reduces to this rule of thumb when advertising
and price elasticities are constant. However, Eq. 5 has the advantage of allowing the selected percentage of sales revenue to adjust according to changing
circumstances.
Advertising elasticity of demand for symmetrically differentiated fi rms is
determined to be
ηAi =
Ai ϕ i (b − ρd )
⋅ 2
qi
b − d2
(6)
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292 System Dynamics Review Volume 25 Number 4 2009
Note that advertising effectiveness and advertising spillover both influence
advertising elasticity. Note also that substituting Eq. 6 for advertising elasticity
into Eq. 5 leads to advertising appearing on both sides of Eq. 5. To avoid
circularity I use the delay feature built into the simulation software to specify
the amount of advertising in the previous period as a proxy for current period
advertising when determining advertising elasticity according to Eq. 6.
Price elasticity of demand for symmetrically differentiated fi rms is determined to be
p
b
ηi = i ⋅ 2
(7)
qi b − d 2
It is relatively straightforward to include the cost of advertising in the model.
Advertising is a cost to the fi rm and reduces profit accordingly. The profit
identity for fi rm i (Eq. 1) now becomes
Π i = pi qi − ci qi − Ai
(8)
Note that the usual microeconomic assumption with respect to production
applies to this model: it is assumed that production can be increased or
reduced instantaneously in order to produce the amount of goods required.
For this reason no formal production function is included in this model. This
assumption implies that there exist no constraints on the instantaneous supply
of human and technological resources to the fi rm. Real systems do, of course,
have lags in providing resources and gearing up the production system to meet
demand change. It is well known that lags lead to oscillatory behaviour and
many system dynamics models focus specifically on these lags (for example,
see Sterman, 1989). Combining a lagged production model with the Cournot
model described above could provide a fruitful area for further research.
The simulation model
The simulation model is based on the analytical model outlined in Eqs 1–8
above. The simulation model works as follows: at any point in time the Cournot–
Nash equilibrium quantity is calculated for both firms according to Eq. 3; price
and fi rm profit are then calculated according to Eqs 2 and 8, respectively. The
optimal amount of advertising is determined for both fi rms using Eqs 5, 6 and
7; advertising then shifts out the demand curve for each fi rm by incrementing
the reservation price according to the flow equation (Eq. 4). These two new
reservation prices create a new competitive situation for the next period of
competition; new equilibrium values are calculated for this next period, and
so on.
The model contains a number of feedback loops that centre on the impact of
advertising on the demand intercept (reservation price). The primary drivers
of system behaviour are the advertising reinforcing loops R1 and R2, which
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M. P. Brady: Advertising Effectiveness and Spillover 293
Fig. 2. Advertising
reinforcing loops
are shown in Figure 2. These loops represent two impacts of advertising:
an increase in quantity placed on the market at the Cournot equilibrium (R1)
and the shifting out of the demand curve and the consequent increase in price
(R2). These loops can be traced by tracking the relevant variables in Eqs 3, 4
and 5 for loop R1 and Eqs 2, 4 and 5 for loop R2.
However, complexity arises in the model because quantity influences advertising in a number of ways. Quantity negatively influences advertising elasticity through Eq. 6, which in turn influences advertising through Eq. 5, generating
balancing feedback loop B1. Intuitively, this balancing loop arises because, as
quantity increases, the relative impact of an amount of advertising decreases.
A second balancing loop, B2, arises because increasing quantity has the effect
of reducing price according to the law of demand (Eq. 2). Balancing loops B1
and B2 are shown in Figure 3. Quantity and price elasticity of demand create
two more reinforcing loops, which are shown in Figure 4.
Fig. 3. Advertising
balancing loops
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294 System Dynamics Review Volume 25 Number 4 2009
Fig. 4. Price elasticity
reinforcing loops
Fig. 5. Causal loop
diagram of cooperative
advertising in a
duopoly
All loops discussed so far refer to each fi rm separately. I now discuss a
number of loops that arise due to competition between the fi rms as shown in
Figure 5. Note that I include in Figure 5 reinforcing loops (R1, R2) and balancing
loops (B1, B2) for each fi rm; I append the letter “a” or “b” to the loop name and
I prefix variable names with “firm” or “rival” to distinguish between the two firms;
to avoid congestion in the diagram I leave out reinforcing loops R4 and R5.
Competition between the two fi rms occurs in three distinct ways. Firstly,
market-level interaction occurs in that quantity placed on the market by both
fi rms influences each fi rm’s price (Eq. 2) and is represented by the pair of
influence links in the upper central section of Figure 5. Secondly, strategic
interaction occurs in that demand for products of both firms (reservation price)
is taken into account when each fi rm selects its Cournot–Nash equilibrium
quantity (Eq. 3) and is represented by the pair of influence links in the central
section of Figure 5. This strategic interaction generates an additional inter-firm
reinforcing loop: an increase in fi rm advertising increases fi rm reservation
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M. P. Brady: Advertising Effectiveness and Spillover 295
price, which in turn reduces rival quantity, which reduces rival advertising,
which reduces rival reservation price, which in turn increases fi rm quantity,
which increases fi rm advertising and so completes loop R3 in Figure 5; I will
refer to this as the strategic interaction loop. Intuitively this loop arises because
when a firm changes its own demand due to advertising its rival must take this
new demand into account in its strategic decision making. This loop only
exists when both fi rms advertise.
The third means by which competitive interaction occurs between the two
fi rms is when advertising spillover occurs, i.e., when advertising by one fi rm
impacts on demand for its rival’s product (Eq. 4). Where advertising is cooperative the effect of spillover is positive; i.e., fi rm advertising increases
demand for the rival product. This influence is shown in the lower central
section of Figure 5 and leads to balancing loops B3a and B3b: an increase in
fi rm advertising increases rival fi rm reservation price, which in turn reduces
equilibrium firm quantity, which reduces the amount of advertising selected. I
refer to these as spillover loops. Intuitively the spillover loops occur because
cooperative advertising increases demand for the rival’s product which, through
strategic interaction, has a detrimental effect on the fi rm itself.
Note that when advertising is predatory the situation reverses: the effect
of spillover on the rival is negative; i.e., fi rm advertising reduces demand
for the rival product. The impact of an increase in advertising is to reduce rival
reservation price, which means that loop reversal occurs: balancing loops B3a
and B3b become reinforcing loops. Loop reversal does not occur during the
course of a simulation run; whether loops B3a and B3b will act as balancing
or reinforcing loops depends on whether the advertising interaction parameter
has a positive or negative sign, respectively. Note that, because I am using
a single parameter for advertising effectiveness, it is not possible for spillover
to be asymmetric: one fi rm cannot advertise cooperatively while its rival
advertises in a predatory fashion.
As can be seen from Figure 5, the causal loop model is symmetric, with the
left-hand side representing the fi rm and the right-hand side representing
its rival. This allows the stock–flow model to be implemented using array
variables of dimension two. The simulation model contains one stock array
variable, one flow array variable, eight auxiliary variables and six parameters,
all but one of which (advertising interaction: the parameter that represents
spillover) are array variables of dimension two. These variables and parameters are listed in Table 1.
The stock variable “advertising_impact_on_demand_reservation_price” is an
accumulator that stores the increase in the reservation price due to the impact
of advertising over time; the flow variable “advertising_impact_on_reservation_
price_rate” controls this accumulation according to Eq. 4. An excerpt from the
stock–flow model showing the stock and flow array variables is shown in
Figure 6. The code controlling the flow array variable in the simulation model
is given below and is directly equivalent to Eq. 4:
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Table 1. Simulation
model variables
Variable
Stock
Advertising_impact_on_demand_reservation_price
Flow
Advertising_impact_on_reservation_price_rate
Auxiliary
Unit_price
Units_demanded
Retained_earnings
Advertising
Revenue
Advertising_elasticity_of_demand
Price_elasticity_of_demand
Parameter
Unit_variable_cost
Own_price_effect
Cross_price_effect_initial_value
Advertising_effect_on_reservation_price
Advertising_interaction_factor
Advertising_weighting_factor
Symbol
Synonym
a
Reservation price
p
q
P
A
R
hA
h
Price
Quantity, demand
Profit
Advertising amount
Advertising elasticity
Price elasticity
c
Cost
b
d
Cross-price effect
j
Advertising effectiveness
r
Spillover
(A switch that turns advertising on or off)
Fig. 6. Stock flow
diagram (excerpt)
RANDOM(1,1) * (Advertising(1) * advertising_effect_on_reservation_price(1)
+ Advertising(2) * advertising_interaction_factor * advertising_effect_on_reservation_price(2)) WHEN F = 1;
RANDOM(1,1) * (Advertising(2) * advertising_effect_on_reservation_price(2)
+ Advertising(1)*advertising_interaction_factor * advertising_effect_on_
reservation_price(1)) WHEN F = 2
where “Advertising” is equivalent to parameter A, “advertising_effect_on_
reservation_price” is equivalent to parameter j and “advertising_interaction_factor”
is equivalent to parameter r; subscripts 1 and 2 represent the array structure
and refer to fi rm one’s and fi rm two’s parameter values, respectively; “F = 1”
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M. P. Brady: Advertising Effectiveness and Spillover 297
indicates the expression for firm one and “F = 2” that for firm two. (Note that the
random function is a provision to allow advertising to have a stochastic impact
on demand but for the purposes of this paper is set so as to have no effect).
The auxiliary variables implement Eqs 2, 3 and 5–8 of the analytical model
and are used to calculate quantity, price, profit, advertising elasticity of demand, price elasticity of demand and advertising amount. Parameters are used
to specify unit variable cost, own price effect, cross-price effect, advertising
effectiveness and advertising interaction. An additional parameter is included
in the simulation model for practical reasons: advertising_weighting_factor is
a switch that allows advertising to be turned on or off at one go without having
to alter a series of parameter values. There is a one-to-one correspondence
between Eqs 2–8 above and the equations underpinning the variables in the
simulation model; Eqs 2–8 were implemented in the simulation model precisely as given above.
Simulation results
The simulation model was used to examine competitive behaviour between
two fi rms when advertising is used as a competitive weapon. The other competitive weapon implicitly used in the model is quantity; however, the quantity decision is not discretionary—firms always make an optimal choice in the
Nash equilibrium sense. This paper assumes that fi rms have some discretion
over advertising and so several advertising-relevant scenarios are examined.
The different scenarios examined in this paper are all generated by changing
just two parameter values: advertising effectiveness and advertising interaction (spillover). I will now discuss three main scenarios: fi rst I examine the
baseline case when neither firm advertises; then I examine the impact of altering
advertising effectiveness; finally I examine spillover of the impact of advertising onto rival fi rm demand.
In order to carry out the simulation the model is initialised by assigning
values to parameters. Unit variable cost c for both fi rms is set at $8, implying
that scenarios examined in this paper refer to a high-volume low-price product, for example a book, an item of clothing, or tin of paint. The initial value of
reservation price a is set at $25 for both fi rms; this means that the highest price
likely to be achieved for the product is $25 even if the good was scarce.
Products are assumed to be symmetrically differentiated and so own-price
effect b is set at 0.0001 and cross-price effect d at 0.00005 for both fi rms. This
implies that 10,000 extra units of product placed on the market will reduce the
price of the product by $1. It also means that the products are differentiated
and the effect of a rival placing a quantity on the market affects fi rm price only
half as much as if the firm itself placed that same quantity on the market. While
parameters b and d appear to be much smaller than those of Perloff’s (2008)
model discussed above, it must be remembered that he represents quantity in
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298 System Dynamics Review Volume 25 Number 4 2009
Table 2. Simulation
model parameter
values
Parameter name
Symbol
Value
Units
Own_price_effect
Cross_price_effect_initial_value
Unit_variable_cost
Advertising_effect_on_reservation_price
Advertising_interaction_factor
b
d
c
j
r
0.0001
0.00005
8
0 < j < 0.000015
−1 < r < 1
$/product unit
$/product unit
$
Dimensionless
Dimensionless
terms of millions of units; normalised to single units Perloff’s parameters
become 0.0000151 and 0.00001 for b1 and b2, respectively, and 0.0000003 and
0.000006 for d1 and d2, respectively. Parameters and their values are summarised in Table 2.
Results for the baseline case where neither fi rm advertises are shown in
Figure 7. This gives the Cournot–Nash equilibrium profits for the industry and
that equilibrium clearly holds for all time. This is intuitively expected as firms
select quantity optimally according to Cournot-Nash and, as there is no change
in the nature of demand over time, will continue to select these optimal
quantities forever.
Advertising is now introduced into the model. First I assume that only one
of the two fi rms advertises. This is achieved by setting the advertising effectiveness parameter for fi rm one to 0.000015, which means that $66,667 of
advertising raises the reservation price by $1. At this relatively high level
of advertising effectiveness the Cournot–Nash equilibrium evolves so as to
drive the non-advertiser (firm two) out of the market, as shown in Figure 8. The
advertising reinforcing loops (R1a and R2a) dominate behaviour by increasing
own fi rm quantity and price. They also act to decrease rival fi rm quantity
through strategic interaction and decrease rival fi rm price through market
interaction. With both quantity and price declining the rival fi rm is gradually
driven out of the market. This is seen in Figure 8, where own fi rm profits
increase exponentially while rival fi rm profits decline. This result suggests
that when an industry is responsive to advertising then unilateral advertising
Fig. 7. Duopoly
with no advertising
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M. P. Brady: Advertising Effectiveness and Spillover 299
Fig. 8. One fi rm
advertises effectively:
j1 = 0.000015; j2 = 0
Fig. 9. One
fi rm advertises
ineffectively:
j1 = 0.000013;
j2 = 0
pays off handsomely. However, this scenario is unlikely to exist for long
in reality as the rival, observing that advertising is effective and yields a
competitive advantage, will also begin to advertise.
As the effectiveness of advertising reduces—either because the fi rm is less
competent at advertising or because the industry is unresponsive to advertising
— a bifurcation in industry behaviour occurs. Trial-and-error experimentation
determined that the threshold level at which industry behaviour bifurcates
lies at an advertising effectiveness of 0.0000139. Below this threshold level
the industry evolves to a stable Cournot–Nash equilibrium, with both fi rms
remaining in the market and with little advantage accruing to the advertising
fi rm; above this threshold the advertising fi rm dominates the non-advertiser
and forces it out of the industry. Figure 9 shows results for a scenario where
advertising effectiveness is set at 0.000013, i.e., below the threshold level.
Balancing loops dominate the behaviour of the system. This result suggests
that when the industry is unresponsive to advertising (or when the firm is poor
at advertising) then there is little advantage to be gained by advertising.
Next I address the more usual scenario where both firms advertise. When
advertising effectiveness for both fi rms is set at a value of 0.000013 then
profitability of both fi rms grows asymptotically, as shown in Figure 10. Advertising is ineffective here, increasing firm performance by less than 2.5%. When
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300 System Dynamics Review Volume 25 Number 4 2009
Fig.10. Bothfi rms
advertise ineffectively:
j1 = j2 = 0.000013
advertising effectiveness is increased above this level for both fi rms then
simulation experiments show that both firms grow exponentially, with growth
driven by the advertising reinforcing loops R1(a and b) and R2(a and b);
for space reasons the results graph for this simulation is not shown but it is
broadly similar to that shown in Figure 12. The results show that industry
performance does not increase linearly with advertising effectiveness but
instead demonstrates a bifurcation in behaviour. This bifurcation occurs at
the threshold level of advertising effectiveness: a value of 0.000013 for the
parameter values used in this scenario. The existence of a bifurcation supports
the empirical observation that a large amount of advertising takes place in
some industries (e.g., soft drinks, beer, mobile phone providers), while relatively little advertising takes place in others (e.g., food staples, clothing). These
results support Borden’s (1947, p. 847) conclusion that “the use of advertising
to increase demand varies markedly among different products” and Davis
et al.’s (1991) finding that the advertising to sales ratio differs significantly for
different industries.
The discussion so far has centred on advertising effectiveness. I now examine advertising spillover. First I consider the case of cooperative advertising.
Here the impact of advertising spillover is positive: advertising by one firm has
a positive impact on its rival’s demand. I use the scenario modelled in Figure
8 where one firm advertises effectively but I now set the advertising interaction
factor r to 0.3. This means that the impact of a fi rm’s advertising on its rival’s
demand function is 30% of that on its own demand function. Cooperative
spillover occurs in reality if, for example, an advertisement for Coca Cola
stimulates demand for Pepsi Cola. The results in Figure 11 show that, in
contrast to those of Figure 8, advertising has little impact on demand: cooperative spillover has the effect of reducing the impact of advertising. This occurs
because spillover increases the reservation price of the rival as well as the
reservation price of the fi rm (Eq. 4) and this higher rival reservation price has
the effect of reducing the optimal quantity selected by the fi rm (Eq. 3), leading
to a reduction in the competitive advantage of the fi rm over its rival. Positive
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M. P. Brady: Advertising Effectiveness and Spillover 301
Fig. 11. One
fi rm advertises
cooperatively
j1 = 0.000015;
j2 = 0; r = 0.3
spillover also reduces the advertising elasticity of demand (Eq. 6), leading to
less advertising being selected (Eq. 5) at the optimal point; less advertising
leads to less of an increase in the fi rm’s demand curve. In terms of feedback
loops, the impact of the advertising loops (reinforcing loop R1a and R2a) is
mitigated by the spillover loop (balancing loop B3a).
Simulation experiments show that, when one fi rm advertises, spillover has
the effect of increasing the bifurcation threshold level of advertising effectiveness. Cooperative advertising reduces the competitive advantage to be gained
through advertising. This suggests that as advertising tends towards being a
public good (i.e., as r → 1) fi rms will be less inclined to advertise unilaterally:
fi rms will not advertise unless other firms in the industry also advertise.
Cellini and Lambertini (2003) drew a similar conclusion with respect to the
public good nature of cooperative advertising. This effect can be seen in reality
when advertising takes place not at fi rm level but at pan-national level (olive
oil in the European Union), national level (milk campaign in Britain and
Ireland), regional level (tourism) or category level (California Avocado Commission: see Wells et al., 2006, p. 112).
I now examine the second possible spillover scenario. Negative spillover
means that advertising is predatory: advertising by a fi rm depresses demand
for its rival’s product. This occurs in the food and electronics retailing industries when advertisers compare their products and prices directly with rivals
with a view to attracting customers from rival stores. Seldon et al. (1993) in an
empirical study found advertising in the cigarette industry to be predatory.
Simulation experiments show that when advertising is predatory the bifurcation threshold level is lowered. This implies that less effective advertisers can
gain competitive advantage over their rivals when advertising is predatory.
Figure 12 shows results for the scenario shown in Figure 10 except that in this
case the advertising interaction parameter is set at −0.3. The results show that
negative spillover has increased the impact of advertising; industry behaviour
has switched and both fi rms grow exponentially. In feedback terms two sets
of reinforcing loops are driving the dynamic behaviour: advertising loops (R1a
and R1b; R2a and R2b) and the spillover loops (B2a and B2b, which have now
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302 System Dynamics Review Volume 25 Number 4 2009
Fig. 12. Two
fi rms advertise
predatorially:
j1 = j2 = 0.000013;
r = −0.3
become reinforcing loops because the advertising interaction parameter has a
negative sign representing predatory advertising). These results suggest that
predatory advertising generates a greater impact on firm demand than does
cooperative advertising.
Discussion and conclusion
John Wanamaker, founder of the department store concept, famously said: “I
know that 50% of my advertising is wasted. I just don’t know which half”
(Black, 2003). This variability in response to advertising is usually put down
to chance or stochastic effects. The results from this model demonstrate that
variability is inherent in a competitive industry system: sometimes the impact
of advertising is strong and the fi rm grows spectacularly and sometimes the
impact of advertising is weak and the fi rm does not grow. Variability is not
induced stochastically: the model is deterministic. Nor is variability induced
by spikes or step changes in parameter values. It is due to system dynamic
complexity and this complexity is inherent in the analytical equations and the
consequent feedback loops.
Different patterns of results occur as initial conditions are varied. The results
show that for some initial conditions reinforcing loops dominate and fi rms
grow and for other initial conditions balancing loops dominate and firms come
to an equilibrium. For yet other initial conditions one fi rm grows and one
stagnates. The results demonstrate that threshold levels of advertising effectiveness exist where industry behaviour bifurcates. When the industry is responsive to advertising, advertising pays off handsomely; when the industry
is not responsive to advertising then advertising yields little competitive
advantage. Such variation in behaviour is not uncommon in complex systems
where loop dominance can change and where dynamic behaviour is not easily
induced from influence diagrams: hence the usefulness of a simulation model
(Lane and Huseman, 2008).
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M. P. Brady: Advertising Effectiveness and Spillover 303
The results also suggest that predatory advertising yields more benefit for a
fi rm than does cooperative advertising. The public good nature of cooperative
advertising can result in competitive advantage being gained by a firm that
benefits from its rival’s advertising but does not itself incur the expense of
advertising. Sice et al. (2000) also examined spillover in the case of research
and development and found that R&D spillover may yield competitive advantage to a fi rm that imitates its rival’s product quality improvements and thus
saves on research and development expenditure.
The Sice et al. (2000) model is of von Stackelberg type, which means that
fi rms make decisions sequentially; this lag effect together with a number of
nonlinearities in the model result in the oscillation of industry leadership and
the chaotic behaviour demonstrated in that model. The model described in
this paper is of type Cournot with firms making decisions simultaneously; this
together with the absence of nonlinearities leads to smoother behaviour over
time. Smooth behaviour is also demonstrated by Wang and Zu (2001) for the
Lanchester differential game and their numerical solution to that game.
From the point of view of feedback loops this is a relatively simple model
with just two stock variables involved in all loops. However, as Figures 7–12
demonstrate, this simple model yields very different dynamical behaviour as
parameter values are varied. Dynamic complexity occurs not so much within a
single simulation run as across different simulation runs.
The simulation model can provide insight into many different competitive
scenarios, the results for only some of which have been presented in this
paper. Different choices of parameter values specifying different levels of
advertising effectiveness and spillover lead to different loops dominating the
dynamic behaviour of the system. High levels of advertising effectiveness lead
to the reinforcing loops dominating and low levels lead to balancing loops
dominating. Some interesting situations occurred where the reinforcing loop
dominating one fi rm led to explosive growth for that fi rm and decay for the
rival fi rm, ultimately driving the rival out of business.
The Nash equilibrium is a game theoretic construct and an interesting aspect
of the model is that it simulates a game theoretic system as it evolves over time.
Figures 7–12 demonstrate the evolution of the Nash equilibrium as it changes
over time due to self-induced system changes. As shown in those figures,
sometimes the situations evolve to an equilibrium (of Nash equilibria) and
sometimes growth in the series of Nash equilibria is explosive.
In this paper cooperative, predatory and zero spillover are precisely defined
in terms of the nature of the impact of advertising on firm demand. Spillover is
independent of actual demand or market share; actual demand is an outcome
of the Cournot competitive process and market share can be viewed as a ratio
of fi rm demands. This approach is in contrast to that typically used in the
marketing literature where category demand (i.e., demand for the entire industry) is calculated in step one and market share in step two: in step one the pie is
enlarged; in step two it is sliced up (Krishnamurthy, 2000). Marketers propose
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304 System Dynamics Review Volume 25 Number 4 2009
two distinct forms of advertising: generic advertising to increase the size of the
pie and brand advertising to increase the fi rm’s slice of the pie; while generic
advertising is usually viewed as being cooperative in nature, and brand advertising predatory, the nature of advertising spillover is not always clear-cut.
In the model described in this paper only one form of fi rm advertising is used
and impact on the rival is clearly defined as cooperative, predatory or neutral
depending on the sign of the advertising interaction parameter: positive, negative or zero value, respectively.
The paper makes a number of contributions. Firstly, the paper clearly spells
out the impact of fi rm advertising and advertising spillover on its competitor by
identifying and examining three different inter-fi rm feedback loops, which I
have termed market interaction, strategic interaction and spillover loops.
Secondly, the paper identifies a bifurcation in industry behaviour as advertising effectiveness passes a threshold level. Significant levels of advertising take
place above the threshold whereas little advertising takes place below it; this
matches the empirical observation that some industries advertise and others
do not. Thirdly, the paper shows that simulation can provide an alternative
to the differential game approach that is often used in the economics and
management science literature to study the dynamic behaviour of fi rms in a
duopoly. While simulation does not yield a closed form solution, once the base
model is created many different scenarios can easily be studied. Also, whereas
differential games usually assume symmetry a contribution of this paper is the
study of duopoly behaviour under advertising when fi rms are asymmetric.
Fourthly, this paper puts forward a system dynamics model of duopoly under
advertising, an underdeveloped area in the field of system dynamics.
A number of avenues exist for future research. In this paper I make the
standard microeconomic assumption that production resources can be instantaneously increased or decreased to meet demand. In practice resources cannot be ramped up or down instantaneously and much managerial effort is
devoted to ensuring that supply matches demand. Indeed many system dynamic models specifically examine the pipeline of resources that together form
the fi rm’s supply chain (see Sterman, 1989, for a description of the well-known
multi-echelon beer distribution model). An avenue for future research is to
enhance the advertising duopoly model suggested in this paper to include a
lead time when increasing the resources required for production. Introducing
such a lag or delay into the model would inevitably stimulate new dynamic
behaviour in the system.
The model also assumes that fi rms can grow exponentially ad infi nitum.
In reality demand is not infinite and at some stage a ceiling to demand will
be reached. The product life cycle concept is based on the existence of such
a ceiling (Milling, 2002). The interplay between boosting demand by advertising and natural decay in demand is another area for future research; the
advertising model of Vidale and Wolfe (1957) includes an exponential decay
factor and could provide a useful starting point.
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M. P. Brady: Advertising Effectiveness and Spillover 305
Acknowledgements
The author would like to thank the editor and two anonymous referees for their
valuable comments on earlier versions of this paper. The author would also like to
acknowledge the support of the W. P. Carey School of Business at Arizona State
University, where much of this paper was written while the author was on sabbatical
leave.
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