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. 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