=Paper=
{{Paper
|id=None
|storemode=property
|title=The Impact of Market Preferences on the Evolution of Market Price and Product Quality
|pdfUrl=https://ceur-ws.org/Vol-627/mass_1.pdf
|volume=Vol-627
|dblpUrl=https://dblp.org/rec/conf/mallow/LiuHD10
}}
==The Impact of Market Preferences on the Evolution of Market Price and Product Quality==
https://ceur-ws.org/Vol-627/mass_1.pdf
1
The impact of market preferences on the evolution
of market price and product quality
Hongliang Liu, Enda Howley and Jim Duggan
Abstract—A significant challenge for firms in an open- challenge. Firms can charge a higher price for their product in
competition marketplace is to balance the conflicting attributes of order to get a higher unit profit. However, higher price levels
price and quality. Higher quality levels tend to lead to increased usually lead to a reduction in customer demand. Therefore,
product costs, which, depending on market preferences, can
trigger an increase in consumer demand. This paper presents a ensuring a good balance between the conflicting attributes of
multi-agent model that allows for an exploration of how price and price and quality is a significant challenge for firms in an
quality evolve as a result of direct market competition between open-competition marketplace.
firms. A new competition model, based on price and quality, is In order to better understand this problem, a number of
defined. Agents compete by determining their price and quality game theoretic models have been proposed [2] [3] [4]. This
levels with a view to maximizing their profit. Our goal is to
examine a range of market configurations and study how agent existing research has focused on the strategic or rational be-
strategies evolve over time. We focus on those factors which havior of competition between two firms. However, what will
contribute to each agent’s survival in this evolutionary setting. happen when there are more than two firms and their decisions
We use game theoretic simulation as a basis to examine various are affected by the effect of bounded rationality? Another
agent strategies. A genetic algorithm is used to characterize a common feature of the current research is that researchers limit
changing environment which evolves over time to reflect the
emergence of fitter strategy attributes. Individuals can evolve their analysis on one market in these models. However, in the
their own market preferences over subsequent generations and real world, firms usually compete with each other in different
adapt to their preferred market strategy. Agent strategies evolve marketplaces. In order to address this issue, we propose a new
rapidly to reflect the bias of their individual market. The price multi-agent competition model, based on price and quality.
and quality relationship of a given market is a primary driver In this model, we consider many firm agents competing in a
of the evolution of agent strategies in that market. Significantly,
our results show the emergence of strategies that prefer low number of markets. Markets are defined by their own unique
price and high quality sensitive markets. This is despite the properties. Price and quality sensitivities are used to represent
penalties which are incurred by the higher costs of increased these properties, and reflect a consumers’ preferred product.
quality. These results have potentially interesting applications to Variations in these values effect the demand of the products
real-world market dynamics, particularly as companies strive to in the market. Different markets may have different price and
position their products optimally on different markets.
quality sensitivities. Each market demand is determined by the
Index Terms—Price and Quality Competition, Agent Compu- average price and quality levels of firm agents in that market.
tational Economics, Agent-based Simulation, Genetic Algorithm Thus, each firm agent faces decision challenges including their
product price and quality levels, and their preferred markets.
Furthermore, the effectiveness of one agent’s strategy depends
I. I on the strategies of others. In this paper, we model firm agents
Consumers from different markets exhibit wide preference as individuals in a genetic algorithm which has been widely
differences due to natural variation in tastes and income used as learning mechanism for economic agents [5] [6]. The
disparities. These are mainly reflected by consumers’ accepted genetic algorithm is also used to characterize a competitive
price and quality levels. For example, consumers in rural areas market environment where the agents compete with each other
may prefer lower price products while consumers in urban for the market share. The firm agents can make price and
areas maybe willing to pay higher prices for higher quality quality decisions and evolve their own market preferences.
products. These consumer preferences can indirectly establish However, they have a limited knowledge of their environment
trends in production. From the view of the firms, higher quality and their performance is largely determined by the actions
usually requires the use of more expensive components, and of their peers. These features of our model are significantly
less standardized production process, and so on. As a result, different with models in the existing research.
higher quality levels tend to lead to increased product costs. In this paper, we aim to examine a range of market con-
Nevertheless, higher quality, depending on market preferences, figurations and study how firm agent strategies evolve over
can trigger an increase in consumer demand, and probably time. We investigate how firm agents strategically position
gain market share [1]. Therefore, there are trade-offs between their products over time and what are the impacts of alternative
quality and cost for firms. In terms of price, it is also a decision market preferences on the evolution. We have conducted a
series of experiments on a range of market configurations.
Hongliang Liu, Enda Howley and Jim Duggan are with the Our results show the impacts of market preferences on the
Department of Information Technology, National University of Ireland,
Galway (email: h.liu1@nuigalway.ie, enda.howley@nuigalway.ie and evolution of market price and product quality. The firm agent
jim.duggan@nuigalway.ie) strategies evolve rapidly to reflect the bias of their individual
2
market. The price and quality relationship of a given market model using decreasing and increasing exponential demand
is a primary driver of the evolution of agent strategies in functions for price and quality, respectively, and analyzes the
that market. Significantly, our results show the emergence of influences of the quality inflating which means that the same
strategies that prefer markets which have low price and also quality performance is worth less tomorrow than today [8].
high quality sensitive markets. This is despite the penalties Recently, Matsubayashi et al. explore the impact of different
which are incurred by the higher costs of increased quality. customers’ loyalty to each firm on the outcome of price and
These results have potentially interesting applications to real- quality competition [4].
world market dynamics, particularly as companies strive to
position their products optimally on many markets. B. Agent based simulations
The sections of this paper are structured as follows. In
Section II, we will review much of the related work relevant Agent based simulations have been successfully applied
to price and quality competition. In Section III, we will many problems such as telecommunications and market strate-
outline our model design. Section IV will provide a detailed gies [9]. In many economic applications, genetic algorithms
examination of our experimental results. Finally, in Section V (GAs) have been widely used to represent the learning pro-
we will outline our conclusions and some future work. cesses of agents [10] [11]. GAs were developed by Holland in
1975 as a way of studying adaptation, optimization and learn-
ing [12]. GAs are inspired by evolutionary biology such as
II. B R
selection, crossover (also called recombination) and mutation.
The study of price and quality competition has attracted A basic GA manipulates a population of chromosomes that
many researchers’ attention. There are two main streams encode candidate solutions to a problem. Each chromosome
in the current research. One is a formal study of rational or individual in a GA is assigned a measure of performance,
behaviors among strategically interacting agents using game called its fitness. In a game context, a chromosome can be
theory. While the alternative approach is to use agent-based interpreted as a strategy, and the GAs processes are models of
modeling and simulation to examine market economies. This is learning. In GAs, the reproduction operator can be interpreted
also known as agent-based computational economics (ABCE) as learning by imitation, the crossover operator can be inter-
which is the computational study of economics modeled as preted as learning through communication, and the mutation
evolving systems of autonomous interacting agents [6]. operator is interpreted as learning by experiment [13].
GAs have been used to examine some well known game
A. Game Theory Models theory models such as Prisoner’s Dilemma [10], Cournot
Since the seminal work of Hotelling [2], a rich and di- competition and Bertrand competition[14]. However, almost
verse literature on price and quality competition has emerged. all the existing research has employed classical game theory
Harold Hoteling analyzes a model of spatial competition which to examine the price and quality competition as we have
demonstrates the relationship between location and pricing examined earlier. Only recently, Tay et al. have used a genetic
behavior of firms. In this model, Hotelling assumes that algorithm to test Hunt’s General Theory of competition [15].
potential consumers are evenly distributed in a linear geo- They consider an oligopolistic market with a number of sellers
graphic location such as a straight street. Consumers have no who are competing on price and a product attribute which
preferences to the firms and only buy products from these that reflects a consumer’s ideal preferences. The sellers’ demand
provides better value in terms of price and transportation cost. function is a linear function of price and and the product
Both firms have the same constant marginal costs and compete attribute which differs from our demand function for markets.
on the store location and price. From this spatial competition Furthermore, we are interested in different research topics.
model, Hotelling argues that the equilibrium strategy for each They aim to use a GA as an alternative simulation method
firm is to choose a location at the center of the market to test a competition theory. Our purpose of this paper is to
which is commonly referred to as “Principe of Minimum investigate the impact of market preferences on the evolution
Differentiation” or “Hotelling’s law”. This argument means of agents’ strategies.
that for any location of one firm, the other firm has an incentive In summary, there is a body of literature in economics on
to move toward its opponent in order to expand the the territory price and quality competition. However, these models rely on
under its exclusive control. In this model, a customer’s location very strong assumptions such as rational behaviour of two
can also be interpreted as a customer’s preference for quality, firms and one market. The research from ABCE has not been
therefore, many papers on price and quality competition are addressed this perspective on price and quantity competition.
inspired by this work. For example, Moorthy considers the In this paper, we propose a multi-agent model and aim to
quality choice in a duopoly, assuming the existence of a address these issues.
quadratic cost function for quality which is different with
the Hotelling’s location model [7]. Banker et al. examine a III. P Q C M
price and quality competition also under a duopoly setting, In this section, we propose our game theoretic model. We
where consumers’ demand is a linear function of price and consider many firm agents competing with each other over a
quality levels and the cost of quality is also a quadratic form number of competitive markets. Different markets may have
[3]. Moorthy and Banker et al. analyze the impact of quality different preferences over price and quality which are reflected
on competitive advantages. Vörös designs a price and quality through market demands in the markets. Firms in the same
3
B. Firm Agents
Market Market Market
In these m markets there are f firm agents in total. Each
firm agent faces decision challenges including their product
C C
C C
C
C C C
C
C
C
C
C C
C
C
C
C
C
C price and quality levels, and their preferred markets. Let ηi =
C
C
C C
C C
C
C C (pi,t , qi,t , ki,t ) denote the agent i’s decision strategies at time
step t where pi,t , qi,t , ki,t are the price level, the quality level and
Firms in the same market compete Different markets have different
the market ki,t (ki,t ∈ [1, m]). The firm agents from the same
with each other on price and quality preferences over price and quality
Firm Firm
marketplace k compete with each other for a higher market
Firm share and profit over time.
Firm Firm
C C C C C
The firm agent i’s market share (si,k,t ) in market k at time
C C C C
C
C
C C
C
C
C
C
C
C
step t depends not only on its own price and quality levels
C
Market Market
but also on the other agents’ strategies. We propose a new
mechanism as follows.
Fig. 1. Price and Quality Competition Model
Dk (pi,t , qi,t )
si,t = w (2)
j=1 Dk (p j,t , q j,t )
where w is the number of firm agents in the market k at time t.
marketplace compete with each other on price and quality This mechanism is different with the mechanisms used in the
for higher profits. As for firms, a relative lower price level existing price and quality competition models [7] [16] [3] [4].
or a higher quality level may attract more consumers. This In the existing models, researchers only consider two firms
depends not only on other firm agents’ strategies but also on competing with each other and one firm’s demand is a linear
the preferences of the markets. Furthermore, the lower price or function of both firms strategies.
higher quality strategies also reduce unit profit level as higher
The firm agents from the same market compete in deter-
quality levels incur higher unit cost levels. Therefore, in our
mining their price and quality levels to maximise their profits.
model, each firm agent faces decision challenges including
The profit (πi,t ) for agent i in market k at time step t is given
price levels, quality levels and their preferred markets as shown
as follows:
in Figure 1. In the following, we first present our market
properties, then the firm agents and their decision-making πi,t = (pi,t − C(qi ))si,t Dk ( p̄, q̄) (3)
process. Finally, our simulator design is outlined. where p̄ = wi=1 pi,t , q̄ = wi=1 qi,t , Dk ( p̄, q̄) is the demand of
market k, si,t Dk ( p̄, q̄) is the firm agent i’s demand, and C(qi )
the agent i’s quality cost.
A. Market Properties Higher quality levels are usually accompanied by higher
We consider m markets. Each market demand is dependent costs in most businesses. In our model, we use a quadratic
on the average price and quality levels (p, q) of all firm agents cost function: C(q) = ǫq2 . The ǫ is a positive parameter. This
in the market. The market demand will increase as the price type of cost function reflects the nonlinear impact of quality
level goes down given any quality level, and on the contrary, it levels on costs and is often used in the marketing literature
increases as the quality of the product improves for any price [7] [3] [4].
level. In order to reflect these relationships in real markets, we 1) Decision-making process: From the discussion above,
use Equation (1) to model market k’s demand Dk (p, q). we note that the firm agents face decision challenges on
their product price and quality levels, and their preferred
Dk (p, q) = Ak e−αk p (1 − be−βk q ) (1) markets (pi,t , qi,t , ki,t ). In this paper, the GA is not only used
to characterize a competitive market environment, where the
where Ak is the potential maximum demand, b ∈ (0, 1], firm agents interact and compete with each other over time, but
αk ∈ [0, 1], and βk ∈ [0, 1] are parameters. Note that the also model firm agents’ decision-making process. In our GA,
demand function is monotonically decreasing over price p each firm agent is represented through an agent chromosome.
and increasing over quality q since ∂D(p, q)/∂p < 0 and This chromosome holds a number of genes which represents
∂D(p, q)/∂q > 0. The combination of the parameters (α, β) how that particular agent behaves.
corresponds to a set of consumers’ price and quality sensitiv-
ities for a given market. Chromosome = (G P , G Q , G M ) (4)
(α) This represents the consumers’ price sensitivity as The G P gene represents the agent’s price decision strategy.
the higher α the demand goes down faster given The G Q gene represents the agent’s quality decision strategy.
the same price change. The higher α means higher Finally, the G M gene represents the preferred market’s ID and
consumers’ price sensitivity. is used to determine which market the agent participants in.
(β) This represents the consumers’ quality sensitivity as Furthermore, we use the profit function as the fitness
the higher β the demand changes faster given the function in our GA (See Equation 3. We do not distinguish
same quality change. Similarly, the higher β value between profit and fitness and will alternatively use both words
reflects higher consumers’ quality sensitivity. in the following context.
4
TABLE I
P .
Variable Range/value Description Variable Range/value Description
T 200 Simulation length β [0, 1] market preference over quality
f 60 Firm agent number 0.05 Selection rate (GA)
m 5 Market number 0.8 Crossover rate (GA)
Ak 6000 Potential maximum demand 0.05 Mutation rate (GA)
b 0.9 Weight parameter GP [0, 5] Price gene
ǫ 1.0 Quality cost parameter GQ [0, 1] Quality gene
α [0, 1] market preference over price GM {1, 2, 3, 4, 5} Market ID gene
In our GA, we use an elitism mechanism to implement our markets have different price and quality sensitivities. In the
selection operator. We select the best agents directly into the following sections, we will firstly examine the results from
following generation which is controlled by the selection rate. homogeneous markets and then the results from heterogeneous
This means, in each generation, a small number of agents do markets.
not change their strategies as their current strategies perform
well. The rest of individuals or firm agents, have a certain
probability to learn new strategies through our crossover oper-
ator and mutation operator. A single point crossover operator is A. Competition in homogeneous markets
implemented. For our mutation operator, the degree of change
of each strategy gene is 0.1 ∗ (max − min) where max and min All 5 markets have the same setting in homogeneous mar-
is a gene’s range. kets. Each market has two parameters α and β which reflect the
market preferences. A high α reflects that a market is highly
sensitive to price, while a high β reflects that a market places
C. Simulator Design
a premium on quality. The results in Figure 2 are from 50 runs
In order to examine the impact of market preferences on of our simulator for each combination of α and β. Figures 2(a),
the evolution of market price and product quality, the GA is 2(b), 2(c), and 2(d) depict the average price, quality, profit and
used to facilitate evolution and a competitive dynamic market demand quantity for the whole agent population at generation
environment. Our competitive market consists a number of 200, respectively.
markets and many firm agents interacting with each other. There are a number of features involving these experiments.
We assume that the firm agents can freely participant in Firstly, we observe that the agents’ average price evolves to
any market, however, one firm agent can only participant a lower level as the α value increases. In other words, the
in one market at each period. The firm agents in the same agents lower their price levels as the market becomes more
market compete with each other. In other words, firm agents sensitive to the price levels. Secondly, the agents’ average
compete locally in a market of their peers, where they have quality level evolves to a higher level as the β value increases.
no knowledge about their peers, or the individual market This reflects that the agents increase the product quality levels
preferences. as the markets pay more attention to quality. Therefore, we
Initially these firm agent genes are generated using a can conclude that agent strategies evolve to reflect the bias
uniform distribution for the first generation. Over subsequent of their market. These emergent phenomena stem from firm
generations new agent chromosomes are generated using our agents’ competition provided by our GA. As the markets
genetic algorithm. For each generation, we firstly calculate are more sensitive to price or quality, the firm agents with
each market’s demand, and then each firm agents market lower price and higher quality products have a competitive
share, and profit (fitness) according to Equation 1, 2 and 3. advantage. These firms are considered the most fit agents in
Finally, the selection operator, crossover operator and mutation our GA. The lower price and higher quality genes are then
operator are applied. Through these operators, a number of promoted in the following generations. Finally, the market
the least fit individuals are removed and replaced with other price and quality evolve to a lower level and a higher level
new strategies which may perform better or worse than those respectively. Furthermore, these strategies subsequently affect
replaced. the average profit as shown in Figure 2(c). Specifically, the
average profit decreases as the markets are more sensitive
IV. E R to price. Higher market price sensitivities lead to intense
In this section, we will present a series of experimental competition, resulting in a decrease in profits. Conversely, we
results from our simulations. Table I shows the parameter observe that the average profit increases as the markets are
settings for the markets, firm agents and our GA. By varying more sensitive to quality despite the higher costs of increased
the different parameters in our model we investigate the impact quality for firms. This is because that higher quality levels of
of market preferences on the evolution of market price and products in the markets result in a higher market demand as
product quality. We examine two different market configu- shown in Figure 2(d), and subsequently an increased profit.
rations: homogeneous and heterogeneous market settings. In Therefore, higher quality has a positive impact on agents’
the homogeneous model, all markets have the same price and profit in our model. This feature of our model is consistent
quality sensitivities while in the heterogeneous model, the with the existing research results [1].
5
5 1
5 4.5 1 0.9
4.5 0.9 0.8
4 4 0.8 0.7
Price 3.5 3.5 Quality 0.7 0.6
0.6
3 3 0.5 0.5
2.5 2.5 0.4 0.4
2 2 0.3 0.3
0.2 0.2
1.5 1.5 0.1 0.1
1 1 0 0
00.1 00.1
1 1
0.20.3 0.8 0.9 0.20.3 0.8 0.9
0.40.5
0.5 0.6 0.7 0.40.5
0.5 0.6 0.7
0.60.7 0.60.7
0.3 0.4 0.3 0.4
α 0.80.9 0.1 0.2 β α 0.80.9 0.1 0.2 β
1 0 1 0
(a) Average price (b) Average quality
3000 800
3000 800 700
2500 2500 700
600
Fitness 2000 2000 Demand 600 500
500
1500 1500 400 400
1000 1000 300 300
200 200
500 500 100 100
0 0 0 0
00.1 00.1
1 1
0.20.3 0.8 0.9 0.20.3 0.8 0.9
0.40.5
0.5 0.6 0.7 0.40.5
0.5 0.6 0.7
0.60.7 0.60.7
0.3 0.4 0.3 0.4
α 0.80.9 0.1 0.2 β α 0.80.9 0.1 0.2 β
1 0 1 0
(c) Average profit (d) Average demand
Fig. 2. Agent behaviors for values of α and β in homogeneous markets
B. Competition in heterogeneous markets which we have discussed in the homogeneous markets. More
interestingly, the effect of quality preferences in heterogeneous
In this section, we examine a scenario where agents compete
markets is different with that in homogeneous markets. For
on price and quality in heterogeneous markets. In heteroge-
example, the quality levels in Market 4 do not evolve to a
neous markets, each market has different price and quality sen-
higher level although Market 4 is a higher quality sensitive
sitivities. Our purpose is to investigate how agents’ strategies
market as shown in Figure 3(b). Conversely, in Market 2, the
evolve over time in heterogeneous markets. The 5 different
quality levels evolve to a higher level although this market has
markets are set as (Market 1: α = 0.1 and β = 0.8), (Market
very low quality sensitivities. This derives from the features
2: α = 0.1 and β = 0.1), (Market 3: α = 0.4 and β = 0.4),
of these markets. Market 4 is very sensitive to price and
(Market 4: α = 0.8 and β = 0.8) and (Market 5: α = 0.8 and
subsequently, firm agents from this market have to reduce
β = 0.1). Each market represents different degrees of price and
their product price levels. This drives their profits down and
quality sensitivities. Our markets have the following features.
consequently, they have lower incentive to produce higher
Markets 1, 2 and 3 have lower price sensitivities while Markets
quality products although consumers in this market prefer
4 and 5 have higher price sensitivities. Markets 2, 3 and 5 have
higher quality products. For Market 2, we can apply similar
lower quality sensitivities, while Markets 1 and 4 have higher
analysis. Finally, we can observe the emergence strategies of
quality sensitivities.
the firm agents that many firm agents enter into Market 1
Figure 3 shows the average data from 50 runs. Figures 3(a), which is a lower price sensitive and higher quality sensitive
3(b), 3(c), 3(d) and 3(e) depict how the firm agents’ average market as Figure 3(e) shows. Although higher quality levels
price, quality, profit, each market demand and the firm agent lead to a production cost, it results in a higher market demand.
numbers evolve over time. From these figures, we notice that In Market 1, agents have to produce higher quality products
the markets’ preferences on price are significant factors on which will incur higher quality cost, but also could stimulate
the evolution of market price levels. As Figure 3(a) shows, the consumer demand. In fact, due to the relationship of price and
price levels evolve to higher levels in Markets 1, 2 and 3 (lower quality preferences, Market 1 becomes the biggest one among
price sensitivities), while in Markets 4 and 5 (higher price the 5 markets (see Figure 3(d)). Furthermore, we find that
sensitivities), the agent price levels evolve to lower levels. This many agents rush into Market 1 which increases the degree
also stems from firm agents’ competition provided by our GA
6
5 1
4.5
Market 1
Market 2 Market 1
4 Market 3 0.8 Market 2
Market 4 Market 3
3.5 Market 5 Market 4
Market 5
3 0.6
Quality
Price
2.5
2 0.4
1.5
1 0.2
0.5
0 0
0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200
Generation Generation
(a) Price (b) Quality
350 2500
Market 1
Market 2
300 Market 3
Market 4 2000
Market 5 Market 1
250 Market 2
Market 3
Market 4
1500 Market 5
200
Demand
Fitness
150
1000
100
500
50
0 0
0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200
Generation Generation
(c) Profit (d) Demand quantity for each market
40
35 Market 1
Market 2
30 Market 3
Market 4
Market 5
25
Agent number
20
15
10
5
0
0 20 40 60 80 100 120 140 160 180 200
Generation
(e) The firm agent numbers in each market
Fig. 3. Heterogeneous markets ( (Market 1: α = 0.1, β = 0.8), (Market 2: α = 0.1, β = 0.1), (Market 3: α = 0.4, β = 0.4), (Market 4: α = 0.8, β = 0.8) and
(Market 5: α = 0.8, β = 0.1) )
of competition. Subsequently, this drives the average profit data is recorded from 50 runs of our simulator over 200
down at the beginning as Figure 3(c) shows. However, the generations. From this table, we can find that the number of
average profit in Market 1 goes up a little due to their learning agents is almost evenly distributed in homogeneous markets
on Market 1’s preferences. Furthermore, we observe that the since there are no differences in markets. The distribution of
distribution of agents in the markets is related to the average agents in heterogeneous markets reflects the bias of agents’
agent profits of the markets. This reflects the agents’s rational preferences which has been analysed above.
choices on market position.
Furthermore, we compare the agent numbers in each market V. C S F W
from homogeneous markets and heterogeneous markets. Table The research outlined in this paper have investigated the
II shows the agent’s distribution in both market settings. This evolution of the price and quality competition under a range
7
TABLE II
A
Homogeneous markets Heterogeneous markets
Market Name
Agent Number Standard Deviation Agent Number Standard Deviation
Market 1 11.9 1.1 36.3 3.0
Market 2 12.3 1.2 14.1 2.7
Market 3 11.8 0.9 6.9 1.8
Market 4 11.6 1.1 2.1 1.5
Market 5 12.4 0.9 0.6 1.1
of market configurations. This research holds particular sig- R
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A
The authors would like to gratefully acknowledge the con-
tinued support of Science Foundation Ireland.