Simulation of Consumers Behavior Facing Discounts and Promotions

Jarod Vanderlynden

1,2

, Philippe Mathieu

and Romain Warlop

Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France

ﬁfty-ﬁve company, 5-7 rue d’Ath

enes Paris, France

ﬁ ﬁ

Keywords:

Consumer’s Behavior, Agent-Based Model, Simulation, Marketing, Pricing Strategy.

Abstract:

Discounts in stores are a powerful tools companies can use to create brand loyalty for products or increase

sales during a short period of time. However, discounts are costly campaigns that result in complex effects

on consumers, yielding unpredictable results and returns on investment. To maintain competitiveness, stores

and brands have to use those campaigns and risk substantial investments. To gain a better understanding

of the impact of discounts on consumer behavior, we argue that it is necessary to complement aggregated

solutions with more granular, individually-centered approaches, such as agent-based modeling. In our study,

we propose a new model based on social and psychological ﬁndings capable of replicating important and well-

known emergent phenomena. This simulation model permits the study of behavioral responses to discounts

and price strategy and can help companies to gain a clearer understanding of the effects of their different

campaigns.

1 INTRODUCTION

In today’s highly competitive business landscape,

companies are well-aware of the indispensable role

marketing plays in driving growth and establishing

brand dominance. Companies have measured the

importance and beneﬁts of promotional campaigns,

including discounts. One of the essential elements

of marketing is offering promotional discounts and

launching campaigns. These efforts not only attract

and retain customers but also position the brand ad-

vantageously in the consumer’s memory. To inﬂuence

behavior, companies design campaigns as effective

as possible by identifying the target population and

the optimal means of promotion. Unfortunately, such

campaigns are expensive and, if not executed cor-

rectly, can be of little use or even negatively inﬂuence

the image of a brand or product. As with many costly

and complex phenomena, measuring the impact of

conceived campaign strategies in a computational lab-

oratory prior to real-world deployment is preferable to

reduce costs and to better align with the potential de-

mand. The use of computational models to evaluate

marketing strategies is well acknowledged. (Negah-

ban and Yilmaz, 2014; Axtell and Farmer, 2022; Said

et al., 2002; Delre et al., 2007; Jager, 2007).

The effects of marketing campaign (marketing

mix (Borden, 1964)) are mainly analyzed by sta-

tistical methods (Tellis, 2006; Wigren and Cornell,

2019) and machine learning algorithms (Tellis, 2006;

Hung et al., 2019) to analyze customer segmen-

tation and to support decision-making. However,

these approaches are limited in understanding the

impact of ﬁne-grained consumer behaviors or sup-

porting exploratory modeling analysis of campaign

strategies under various scenarios. We argue that

Multi-Agent Systems (MAS) perspective with its

individual-centered approach via Agent-Based Mod-

eling (ABM) facilitates the design and calibration of

behaviors at a level of detail that allows a better un-

derstanding of the factors facing a marketing cam-

paign. We also show that such an approach allows

easier adaptation to changes in the environment such

as the arrival or change of a product, thus providing

robust and exploitable results.

In this article, we consider the context of a super-

market with the objective of understanding the con-

sumers’ behaviors through their adaptive reactions

over time to changes in prices or packaging of prod-

ucts. To do so, we propose a model focused on in-

dividuals, allowing the deployment of promotional

campaigns at a chosen date and duration through sim-

ulation, and measuring its impact on various popula-

tions. The great diversity of customer behaviors and

promotional campaigns (price reduction, a percentage

discount, vouchers, purchased/offered lots) motivates

260

Vanderlynden, J., Mathieu, P. and Warlop, R.

Simulation of Consumers Behavior Facing Discounts and Promotions.

DOI: 10.5220/0012320300003636

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 16th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2024) - Volume 3, pages 260-267

ISBN: 978-989-758-680-4; ISSN: 2184-433X

using ABM.

The rest of the paper is structured as follows. In

the ﬁrst part, we present the state of the art and high-

light the signiﬁcance of exploring the link between

price evolution and consumer behavior. In the second

part, we present an ABM for testing discount cam-

paigns that rely on an individual utility function that

each agent uses to evaluate products. The third part

describes the design of computational experiments

performed along with the results in relation to loyalty

and sales volume evolution. Finally, the last part dis-

cusses the model’s advantages, potential extensions,

and future research avenues it affords, including con-

sidering social inﬂuence.

2 BACKGROUND: ABM IN

MARKETING RESEARCH

The study of marketing strategies through simula-

tion is not new. Prior research often relied on using

equation-based or statistical approaches. Research on

individual-centered ABM approaches highlighted the

signiﬁcance of behavioral differentiation. (Negahban

and Yilmaz, 2014; Axtell and Farmer, 2022; Said

et al., 2002; Delre et al., 2007; Jager, 2007).

• In (Delre et al., 2007) the launch of a prod-

uct in a population is inﬂuenced by word-of-

mouth (WOM), and The interaction possibilities

are modeled via a ”small world” (Watts–Strogatz)

graph. In the model, when an agent adopts a new

product, it tries to convince its neighbors to do the

same. Word-of-mouth is a complex phenomenon

and the models that study it integrate graphs to

represent notions of social contacts, which agents

can inﬂuence. We consider word-of-mouth, or in

general social inﬂuence, is an area of study that

offers new avenues of research but is not the pri-

mary focus of our current research objective. The

confounding effects of the word-of-mouth mecha-

nism with price dynamics would reduce the inter-

pretability of the results, so we are primarily in-

terested in understanding the impact of prices on

different behaviors.

• There exist guidelines for modeling various mar-

keting aspects in ABMs In (Negahban and Yil-

maz, 2014), the authors propose an approach

based on evaluating products according to a util-

ity function. This allows model agents to evaluate

items differently according to their characteristics.

Thus, it becomes possible to create and modulate

the characteristics of the agents, to reproduce be-

haviors classically observed in marketing.

• The use of ABM with individual behavioral pa-

rameters that regulate the diffusion of products

is discussed in (Said et al., 2002). By exploring

the parameter space, the authors reproduce styl-

ized facts about consumers’ brand choices, such

as the emergence of an equilibrium between mar-

ket shares and a lock-in effect of the market shares

of a dominant brand or a cyclical competition be-

tween dominant brands.

• In (Jager, 2007), the authors apply marketing el-

ements, including product, price, place of dis-

tribution, and promotion, in a social simulation

model centered on individual behavior. In their

model, agents have both individual and social

preferences. Individual preferences are deﬁned by

the characteristics of each agent and social prefer-

ences are determined by looking at the consump-

tion of socially connected individuals in a random

graph. These four characteristics are fundamental

in marketing and originate in (Borden, 1964).

However, it should be noted that the models pre-

sented in (Delre et al., 2007; Said et al., 2002) do not

explicitly integrate the price component, and that (Ne-

gahban and Yilmaz, 2014; Axtell and Farmer, 2022;

Jager, 2007) do integrate the price, but are mainly in-

terested in social inﬂuence without studying the price-

behavior link, which is the central point of our work.

Some properties are generally easier to model with

ABMs than equational models. This is notably the

case of social inﬂuence dynamics which requires ex-

plicit links between different individuals, as opposed

to the notion of advertising, which can be explored

with an equational model.

2.1 Modeling Individual Behavior

The modeling of a purchasing behavior process is

based on two fundamental aspects: internal inﬂuences

(characteristics speciﬁc to each individual that inﬂu-

ence the desire to buy a given product) and exter-

nal inﬂuences (e.g., advertising, promotion, word of

mouth). In this work, we focus only on internal inﬂu-

ences and price dynamics. It seems natural for most

authors to use the price and quality of each product

as an internal inﬂuence. (Hardie et al., 1993; Bawa,

1990; Seetharaman and Chintagunta, 1998; Cohen

et al., 2020) propose to add additional criteria: loss

aversion or inertia.

• loss aversion (prospect theory), is predicated on

the notion that losing 1$ has more impact on a

consumer than gaining 1$.

• inertia or brand loyalty, suggests that a consumer

will not necessarily take the ”best” product of-

Simulation of Consumers Behavior Facing Discounts and Promotions

261

fered, because it is also inﬂuenced by habitual be-

havior and brand loyalty.

(Hardie et al., 1993; Cohen et al., 2020) sug-

gest using a reference product to consider loss aver-

sion. This can be speciﬁc to each individual in a

MAS model. The inertia can be simply considered

by a reinforcement process or preferential attachment

(Bawa, 1990; Seetharaman and Chintagunta, 1998).

These aspects can be combined through a utility func-

tion used when evaluating a product ((Negahban and

Yilmaz, 2014)). To combine these different notions,

(Negahban and Yilmaz, 2014) suggests summing up

the behaviors taken into account with a utility func-

tion used when evaluating a product.

2.2 The Impact of Promotion

Promotions undeniably increase sales volume (Blat-

tberg et al., 1995) and induce asymmetrical impact on

other products, along with diminishing returns on re-

peated promotions. The confounding effects of these

different aspects motivate our work on evaluating a

promotional campaign model. To this end, our model

builds on an individual-centered modeling framework

(Negahban and Yilmaz, 2014; Axtell and Farmer,

2022; Said et al., 2002; Delre et al., 2007; Jager,

2007) and augments it with loss aversion and inertia

as (Hardie et al., 1993; Bawa, 1990; Seetharaman and

Chintagunta, 1998; Cohen et al., 2020) to exhibit the

classical impact properties of promotions described

by (Blattberg et al., 1995).

3 SPECIFICATION OF THE

MODEL

In this article, we focus on a model of a store by which

it is possible to simulate different discounts on dif-

ferent products. For example, a percentage reduction

in price or a ”by three get one free promotion”. The

model is also capable of reacting to price changes out-

side a temporary promotion, or to the arrival of new

products in the store. In this model, there is no spatial

representation, the agents are omniscient and know all

the products and their characteristics. We do not take

into account the geographical positioning of the store

and the products, nor the social inﬂuence, in order to

focus on the inﬂuence of price and promotions.

We start by presenting the packs (products) and

the agents that constitute the store’s customers, fol-

lowed by the speciﬁcation of the environment that

characterizes the store and its products. The model

dynamics is based on a behavioral model, involving

the strategies and mechanisms used by agents to rea-

son and make decisions about product selection.

3.1 The Product Model

A ”pack” represents any product in a supermar-

ket. This product can be sold alone or in a pack.

This information is represented by the characteristic

quantity In our model, it is represented by a quadru-

ple, P(p, Qte,Qa, D):

• p represents the price,

• Qte is the quantity of product in one pack,

• Qa is the level quality,

• D represents a boolean variable indicating if there

is a discount.

For more realism, products are regrouped into dif-

ferent categories. Let C = c

, c

, ... be a set of product

categories. Let C

= P

, P

, ... be a set of products rep-

resenting a product category. Each pack belongs to a

category C

∈ C = C

, ...

∀P

∃C

∈ C

∈ C (1)

The objective of the different agents is to choose,

at most, one product in each category.

3.2 Customer/Agent Settings

An agent, a(H

, λ

, P

re f

, (β

, β

)), represents an

entity (a person, a family or other) who shops regu-

larly in the store. Its behavior is based on its habits.

An agent is characterized by internal parameters that

differentiate it from its peers and individual history

and cognitive references for each category. Let:

• l

the length of the purchase history considered by

the agent. (sliding window)

• H

i,a

a list of packs for each category correspond-

ing to the purchase history.

i,a,t

The product purchased by agent a in category

at time t H

i,a,t

= P

i,a,t

at initialization H

i,a

i,a,−l

, P

i,a,−l

, ..., P

i,a,−1

}. At time t = l

i,a

= {P

i,a,1

, P

i,a,2

..., P

i,a,l

• λ

i,a

the need for each category C

• P

re f ,i

a reference product by category C

as in

(Hardie et al., 1993)

• β

, β

Sensitivity to price, quality, inertia

(the strength of habits) and promotions.

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

262

3.3 The Environment

The environment represents the store which includes

the agents and the products. The agents interact with

the environment by buying products. We use the envi-

ronment parameters to modulate the global function-

ing of the model, e.g., increasing the signiﬁcance of

promotion or increasing the capacity of loss aversion.

The environment is therefore characterized by the fol-

lowing properties:

• β is the loss aversion parameter (identical for price

and quality), β > 1.

• C deﬁnes limit for the purchase quantity, C >= 1.

• α

sat

represents the saturation parameter.

• l

is the length of the purchase history.

• G

, G

represent the impact regulation pa-

rameters: price, quality, inertia, and promotion

(discount).

Figure 1: UML Conceptual Structure of the Model.

3.4 Hypothesis

We consider products as everyday consumer goods,

which allows us to hypothesize that purchases are fre-

quent and therefore that at each time step each agent

questions the purchase. We could consider that a time

step represents a week and that each customer arrives

at the store each week to shop. It is assumed that the

need (the λ

i,a

) is computed using the average history

of the quantities purchased: λ

i,a

= mean(H

i,a

(qte)).

We exclude purchases of different packs in the same

category to simplify the choice of agents. This is

equivalent to excluding the purchase of two similar

packs, but of different brands. Each agent chooses,

at each time step, at most one pack in each category.

This assumption does not prevent agents from buy-

ing the same pack multiple times or from not buying

anything.

3.5 The Strategy for Choosing Packs

The strategy for pack selection depends on the pref-

erences of agents. Agents can have distinct choices

depending on their valuations.

3.5.1 Agent Preferences

At each time step, agents determine if they need a

product of a speciﬁc category. An agent a evaluates

, by computing B(C

,t +1), the probability of need-

ing a product of this category at time t + 1. Finally,

N(C

,t,t − n) is the quantity of the product the agent

purchases in the last n steps.

sigmoid(x) =

1 + e

−x

(2)

B(C

,t + 1) = sigmoid(

i,a

N(C

,t,t − n)

) (3)

Intuitively, this formula allows agent a to increase

the probability of being interested in category C

if it

has purchased a small amount over the last few steps

and inversely to reduce this probability if it has pur-

chased more than usual lately.

3.5.2 The Evaluation of Packs

When an agent is interested in a product category,

it evaluates all the packs, gives them a score, and

chooses one. A high score means that the product

matches the agent’s expectations and is more likely

to be chosen. The probability of purchase is propor-

tional to the scores of the packs. For example, if we

take 3 packs A, B and C with a score of 12, 6 and 2

respectively, the probability of purchase distribution

will be 0.6 for A, 0.3 for B and 0.1 for C. Let c a pack

category, P

a pack within c, Pr

the probability of

the pack P

to be chosen and score

the score of the

pack.

score

∑

i∈c

score

(4)

To give a score to the packs, the agent uses his

sensitivities and the parameters of the packs.

We deﬁne four utility functions U

, one

for each evaluated characteristic, respectively: price,

quality, inertia, and promotion. The ﬁrst two U

and

compare the pack being evaluated with the refer-

ence pack on price and quality. It’s in these formu-

las that loss aversion is taken into account. The third

one considers the inertia, similar to the speciﬁcation

presented in (Bawa, 1990). Finally, the last func-

tion calculates the impact of a promotion. We then

weigh the results of the four previous functions by the

agent’s sensitivities. The aggregate utility determines

the score of the pack for this agent. The higher the

score, the more the agent is interested in the pack.

(x)

represents the maximum between 0 and x.

Simulation of Consumers Behavior Facing Discounts and Promotions

263

= G

× (β × (p − p

re f

)

+ (p

re f

− p)

) (5)

= G

× (β × (q − q

re f

)

+ (q

re f

− q)

) (6)

= G

× (10 × nb

bought

− nb

bought

) (7)

= G

× D (8)

We note that the impact of the price decrease is

calculated in U

and not U

. We model with U

only

the impact of the presence or not of a promotion.

U(P, a) =

∑

k=1

∗ β

a,k

(9)

3.5.3 The Purchase Quantity

Calculating the quantity purchased is independent of

the internal quantity of each product. This calculation

is used to decide the number of packs bought by the

agent for the chosen pack. If P(p, Qte, Qa, D) is the

chosen product, and Qte is 100g, then the agent will

use the formula 10 to calculate the desired quantity.

The agent then buys three times the same product. In

this formulation, N(C

,t) is the quantity purchased at

time t of C

Buy(P,t + 1) = max(1, λ

i,a

+ N) × S (10)

N =

∑

τ=0

i,a

− N(C

,t − τ)

T + 1

) (11)

S = Sat(U(P) −U (P

re f

,t)) (12)

Sat(x) =

1 + e

−

sat

+log(C−1)

(13)

3.6 The Dynamics of the Model

The Choose method chooses a pack using a probabil-

ity distribution proportional to the pack score. The Qt

method uses equations 10 to 13 to compute the quan-

tity that the agent a buys.

A trace of the execution of this algorithm can be

found in the Jupyter sheet available at this address:

https://github.com/cristal-smac/retail

4 EXPERIMENTS

In this section we show the model is capable to re-

produce known marketing phenomena. All our ex-

periments are performed with the same environmen-

tal parameters. On the same experiment, the agents

and products have the same characteristics to allow

Data: A the sets of agents;

C the sets of packs category;

(i,a,t)

the history of what agent A bought on

category Ci at time t;

Result: Decision process used by each agent.

t ← time step t;

for all agents a ∈ A do

a go to the store;

for all category c

∈ C do

(i,a,t−l

)

← None (delete);

p ← B(c

,t + 1);

x ∼ U(0, 1);

if x > p then

(i,a,t)

← (None, 0)

else

for every product p ∈ c

score(p) ← U(p, a);

l append (score(p), p);

end

i,a,t

← Choose(l);

q ← Qt(Chos, re f );

(i,a,t)

← (Chos, q);

end

Algorithm 1: Decision process.

comparison. The procedure to generate the agents and

products are randomized procedures. The agents are

categorized according to their sensitivities. All ex-

periments are performed several times (20) for more

accuracy. We show that in the same situation (similar

agents and products), two identical promotions have

almost the same effect.

The model is able to reproduce classical macro-

scopic promotional phenomena in marketing such as:

• The increase in the volume of sales of a product on

promotion. This effect is fundamental according

to (Blattberg et al., 1995).

• Cannibalization, which corresponds to the de-

crease in sales of products competing with a prod-

uct discounted during a discount.

• Repeated promotions on the same product have a

lesser impact with each new promotion.

But above all, the model can reproduce phenom-

ena that are observable only at the level of the agents,

impossible to observe with an approach that would

not be centered on the individual, such as :

• Multiple successive promotions change the refer-

ence price of the agents.

• The price war is a phenomenon with macroscopic

impacts, but also microscopic impacts by chang-

ing the perceptions that consumers have of certain

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

264

Figure 2: Quantity of sales as a function of time in a simu-

lation. On the left without a promotion, on the right with a

promotion of 40% between time steps 30 and 34.

brands. This inﬂuence also has effects on the loy-

alty of consumers to certain brands.

• How promotion impacts the acquisition and re-

tention of new consumers, especially according

to different proﬁles. For example, a promophile

consumer will regularly change products if they

are on promotion.

Within our experiments, it is discerned that the

model adeptly reproduces renowned effects with con-

siderable precision, thereby afﬁrming the validity of

our methodology.

4.1 Decline in Sales Volume of Other

Products

The decline in sales of products that are not on pro-

motion is also a common phenomenon. It is said that

the promoted product ”cannibalizes” the sales of other

products of the same type. This effect can be seen in

Figure 3. The drop in sales of non-promoted prod-

ucts ranges from 2 to 20 percent on average and varies

by product and by similarity to the promoted product.

The drop varies by the number of product in the cate-

gory too. At least 1 product always has a sales decline

of more than 0 percent.

4.2 Impact of Repeated Promotions

The model also shows the frequency of promotions

wields a profound inﬂuence on their efﬁcacy. A satu-

ration of promotions tends to attenuate the peak sales

they typically induce. This can be attributed to the

evolving consumer evaluation of products; as they

grow accustomed to incessant discounts, their propen-

sity to transition between products during a discount

diminishes. This effect can be seen in our model as

described by 3

4.3 Testing the Robustness of the Model

To test and show how the model can behave, and it’s

adaptation to different cases, we make 3 other test :

Figure 3: Quantity of sales as a function of time in a simu-

lation with a promotion of 40% on the Pack 0 between time

steps 30 and 34.

(a) Evenly distributed pro-

ﬁles.

(b) Only discount oriented

agents.

ented agents.

(d) Only inertial/loyal

agents.

Figure 4: Simulations of 100 time steps, making a 40% dis-

count between time step 30 and 34 on all simulations. We

very the sensibilities of the agents in each simulation. In

4a a simulation with the 5 proﬁles presented earlier evenly

distributed. In 4b a simulation with only discount oriented

agents (promophile). In 4c a simulation with only price,

quality oriented agents and ﬁnally in 4d a simulation with

only inertial/loyal agents.

what happens when proﬁles of agents change, how the

duration of discount impact the results and we test the

difference between a temporary price reduction and a

discount.

4.3.1 What Happens when You Change the

Behavior/proﬁles of Agents

We vary the proportions of the different agent pro-

ﬁles and test new ones to observe the effects of these

agent’s parameters on the model.

On simulations in ﬁgure 4 we observe that the pro-

Simulation of Consumers Behavior Facing Discounts and Promotions

265

Figure 5: Simulations of 100 time steps, making a 20% dis-

count between time step 30 and 34 on the left and a 20%

discount between time step 30 and 50 on the right.

mophile proﬁles are very impacted by the promotion,

but are also more likely to be loyal. Indeed, on the

same promotion of 40% on the same time steps with

the same agents and the same packs, we observe a

short term increase in sales of 78% for the promotion

on classic proﬁles against 116% for the promotion on

only promophile proﬁles. Similarly, in the long term,

we see an increase from 28% for classic proﬁles to

79% for promophile proﬁles. Finally, if price and

quality agents’ sensibilities are exacerbated, we ob-

tain agents who are very oriented towards the qual-

ity/price ratio. This ratio is better during a promotion,

which means that we always see an increase in sales

during the promotion, but since the agents are very

oriented towards the quality/price ratio, they tend to

quickly turn to the pack with the best ratio. Finally,

the so-called inertial or loyal agents are not impacted

by the promotion. These simulations show that a vari-

ation of the agents’ sensitivities leads to different re-

sults, but always consistent with what we model.

4.3.2 The Impact of the Duration of a Discount

The duration of a discount corresponds to the number

of ticks the discount lasts. The simulations of ﬁgure

5 shows longer discounts have greater impact. The

long discount last 20 ticks compared to 4 ticks for the

other. However, it is important to note that we go from

a peak sale of 78% to a peak sale of 110% for the same

amount of discount. Finally, the length of the promo-

tion leads to a stronger loyalty. Indeed, the inertia has

time to set in, the customers have in a way made the

product part of their consumption habits.

4.3.3 The Difference Between a Temporary

Price Reduction and a Discount

Figure 6 shows the difference between a discount and

a temporary price reduction. A price reduction that is

not posted as a discount has less impact. The short-

term impact of the promotion is 76% additional sales

(during the promotion) versus 45% for the discount,

and the long-term impact is 28% additional sales for

the promotion (loyalty) versus 20% for the discount.

Indeed, promophile agents do not perceive this dis-

Figure 6: Simulations of 100 time steps, making a 20% dis-

count between time step 30 and 34 on the left and a 20%

price reduction between time step 30 and 50 on the right.

count as a promotion. Only price-oriented agents are

really sensitive to this kind of change.

5 MODEL CAPABILITIES

In this section, we explore the practical applica-

tions of our model and demonstrate its ability to

inform decision-making processes in pricing strate-

gies. Leveraging the power of computational simu-

lation, we uncover valuable insights into optimizing

discounts : when to apply them, how much to offer,

and the interplay of competitive products in the mar-

ket.

We propose an experiment involving 3 packs

of the same category, directly competing with each

other. It is noteworthy that the price-quality ratio is

the same for each of the packs to avoid a domination

of one pack in the simulation. The number of simu-

lation time steps, the number of agents, their parame-

ters, and the timings at which promotions for packs B

and C are carried out are ﬁxed. The goal is to test var-

ious promotions for pack A, calculate the proﬁts (the

selling price minus a lower value representing the cost

of the pack) for this pack, and determine the best pro-

motions to carry out.

To test different promotions, we initially con-

ducted a random search and then implemented a ge-

netic algorithm. We justify the use of a genetic al-

gorithm because the number of possible promotions

is very large and we cound’t ﬁnd the optimal solu-

tion in a reasonable time. In this experiment, in each

simulation, we propose conducting up to 10 different

promotions for Pack A throughout the simulation at

variying time steps. Given the simulation duration of

100 time steps, there are up to C

100

possible promo-

tion moments and 100

possible promotion power (in

%). Even when excluding promotions at a loss, this

number remains substantial.

Firstly, it emerges from this experiment that in our

model under these experimental conditions, it is more

proﬁtable for the proﬁts generated by pack A if its

promotions do not coincide with the promotions of

packs B and C. Additionally, we observe that con-

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ducting a rather strong promotion (around 40%) at the

very beginning of the simulation, from time steps 0 to

10, increases the proﬁts of Pack A. It is noteworthy

that there are no other promotions on packs B and C

at this speciﬁc moment. Finally, the model demon-

strates that it is necessary to conduct at least a second

promotion later in the simulation, often just after the

promotions of B and C, to prevent these promotions

from impacting the sales of A.

In conclusion, our experimental ﬁndings suggest

that, within the speciﬁed experimental conditions of

our model, it is more advantageous for the proﬁts gen-

erated by pack A to schedule its promotions indepen-

dently of those for packs B and C and to use the pro-

motion sparingly.

6 DISCUSSION

In this paper, we show in section 4 that the agent-

based approach proposed in section 3 is able to repro-

duce emerging phenomena known in marketing such

as the increase in sales volume, the ”cannibalization”

linked to competition or the changes in customers be-

havior caused by the rapid repetition of promotions.

Moreover, the individual-centered approach allows us

to show phenomena that are only observable at the in-

dividual level, such as loyalty during a promotion or

the effects of price wars directly on consumers. We

show the model’s ability to reproduce general stylized

marketing facts and to adapt to different scenarios. In

this way, we propose a form of learning that allows

us to start from a known scenario, and run a complete

simulation of different scenarios that we would like to

explore. Scenario exploration is facilitated by access

to simulated data similar to real data (sales receipts).

In order to deepen the model, it is possible to add

a system of social inﬂuence similar to those described

in the section 2, which would allow agents to ex-

change and interact with each other in order to in-

ﬂuence each other. Moreover, it is possible to give

the agents only a partial knowledge of the products,

so the agents would have to discover themselves the

products they do not know or be socially inﬂuenced.

Finally, it would be interesting to study the notion of

similarity between products and to see, according to

this similarity, the competition generated and the ef-

fects of promotions.

The proposed model has the possibility to easily

integrate real data (via history) which would improve

the realism, and apply the model to concrete scenar-

ios. We justify its adaptability to the data through the

global parameters built into the model.

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