Modelling Demand for Innovative Products Marco Valente [email protected] Department of Economics University of Trento, Italy

EARLY DRAFT

Abstract This paper deals with demand, a (too) frequently neglected aspect of economic theory. It is introduced, described and discussed a simulation model that, mirroring most models in industrial dynamics, provide a very stylised representation of supply and a relatively detailed, although highly general, account for demand. The model does not represent the aspects that influence exogenously demand, like social classes and particular preferences. Rather, assuming every aspect identical for all agents, considers the endogenous dynamics springing from the very development of the market. The core aspects of the model are the algorithm implementing the purchase decisions of buyers, and the endogenous formation of preferences. The former aspect is represented with a bounded rational algorithm based on the lexicographic preferences. The latter is based on the effects of the marketing strategies of producers, biased with information diffused in the society concerning the different products. The exercises discussed do not aim at provide a realistic representation of real observations, but on showing how even such an abstract set-up is able to represent phenomena that are normally either ignored, or assumed as exogenous in the literature. In fact, the use of simulation models allow not only to assess the final outcome of the model, but also the pattern and the microexplanations of the observed results. Although the model discussed has been highly stylised for the purpose of better presenting its content and results, it may be obviously extended in many different ways. In the conclusion are briefly listed few of the possible extensions of the model in fields where the analysis of demand plays a crucial role.

Paper presented at the International J.Schumpeter Society Conference, Manchester, June 2000.

Introduction One is not too far from the truth saying that the demand side of markets is a forgotten field in economic theory. Few (potentially) seminal works in the past (Veblen, 1899, Lancaster, 1966) obtain a sort of ritual respect in the citations, as they justly deserve, but remain hopelessly without followers or developers in the economic academy. This may be justified if, as neoclassical standard economic says, the (exogenous) preferences and perfectly rational behaviour determines all we need to know from demand. If one does not accept this theory1, few alternatives are available. Recently, a number of works that acknowledge such deficiency appeared in the literature, attacking the problem from diverse perspectives (see, e.g., Metcalfe, 1998, Aversi et al., 1999, Cowan et al.. 1997, Devetag, 2000). Simplifying, these proposals for a theoretical account of demand in economics can be divided in two groups: one focused on the social determinants of demand behaviour, and the other on the psychological ones. This two, naturally compatible, proposals analyse the effects that social or psychological events have on demand. Even in very simple cases, it is shown that the assumption of socially, or psychologically, differentiated individuals provide a rich wealth of economic phenomena, and therefore deserve to be included in the repertoire of economists. In this work, I try to contribute to the list of features that a theory of demand should include. It is suggested to include in the theoretical analysis few aspects, that are of obvious importance for any account of historical events. While in economics a product in a market is represented by price only (i.e. homogeneous products), or, at most, by price and quality, in the real world we see products with many different aspects, each of which may be the most appealing for some class of buyers. Therefore, the first contribution is to stress the multidimensional space of product qualities, and a proposal to tackle the numerous problems that arise from such consideration2. The second contribution is, again, inspired by real world observation. Whatever is the products typology and the market they are involved into, it seems that companies cannot help spending huge sums in advertisements, or marketing initiatives in general. Many of the explanations concerning historical events frequently cite the success or the failure of marketing strategies as the crucial culprit. Moreover, even a superficial consideration shows that marketing expenses rank among the 1

Although it is not a goal of this work to list the fallacies of neoclassical consumer theory, it may be worth to underline only one, possibly the most important. The use of the rationality assumption, falsified by observation, is kept only under the as if hypothesis. But this hypothesis requires at least a minimally effective selection pressure, which cannot be considered at all among consumers: irrational consumers are never selected out of the market. 2 There are a number of technical ways to consider formally many dimensions but doing actually with only one, like using a system of weights that provide a sort of “cross elasticities” to squeeze all the dimensions in a unique one. However, such systems have no comfort from the observation of real world cases, and, removing the problem together with the advantage of multi-dimensional products, do not provide much greater results than models with homogeneous products.

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top positions in the modern companies’ accounts. Economic theory has close to nothing to say on such important phenomenon. This work contains a proposal on how marketing may be included in the economic thinking, and describes few early results obtained with such proposal. The basic thesis is that companies promote marketing initiatives in order to induce consumers to adopt particular visions of the product typology, such as to favour their own product against competitors’. In other terms, companies influence strongly buyers’ preferences, which, therefore, cannot any longer being considered only as exogenous inputs in economic models. The proposals briefly described above are implemented in a computational model. This methodology is chosen because it leaves the largest freedom to the modeller. Moreover, it is unique in that allows to explicitly represent differentiated timing for the model’s events, where some take place more or less frequently than others. As it is suggested, although not fully discussed, the timing of events in simulation models are often underestimated as determinants of results, although the experience of real observations shows that frequently the time factor is crucial part to fully understand historical observations. Although not discussed in the detail, underlining all this work is a proposal for a methodology of computer simulations in economic theory (see Valente, 2000). The methodology is based on the opinion that implementing an algorithm aimed at representing a given phenomenon with a computer language is, just on itself, a very effective way to test its viability. In fact, a modeller tends to consider “statically” the different equations of the model, and only when they must be implemented in a program the inconsistencies or hidden assumptions become clear. This happens because computer languages have embedded a very strict discipline not only on how to represent a given algorithm, but also on when it should be activated within the simulated flow of time. It is therefore wise not to delegate the programming to “experts” which, almost inevitably, will introduce arbitrarily extra-assumptions in the model. Simulation models, after being implemented, are used as sorts of “toy worlds” where alternative histories are produced, compared and investigated. Therefore, it is not the statistical robustness a criterion for judging the validity of the results, but their capacity to provide insights on phenomena that cannot be investigated with other instruments This implies that it is not possible to present few stability index to “proof” the results of a model, but it is necessary to “explain” its results in detail, and, quite necessarily, to allow suspicious readers to use the very simulation program in order to replicate the results. This, of course, poses an even larger burden on the modeller, that not only

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needs to write the simulation program, but also to provide it with the set of interfaces to allow others to use it3. The presentation is divided in three sections. First, a brief accounts of the basic motivations behind this work is presented. Then, a computational model is presented, and, lastly, some of the results provided by the model are discussed.

A minimal model for supply The goal of this work is to study the aggregate properties of markets stemming from the demand side, and therefore the representation of supply is purposefully stylised and "frozen". However, even though we want to avoid supply's dynamics making difficult the investigation of demanddriven phenomena, we need to represent products and producers' behaviour in such a way to make possible the study of aggregate consumers' dynamics. That is, we need that to model the "interface" of supply as observed by the demand side of markets, even neglecting the underlining mechanisms determining the emergence and dynamics of producers. This means that, for example, the model will not consider any production costs, investment, technological innovation etc., but only their final outcome embodied in the products' representation as observed by consumers. It is worth to repeat that this assumption is merely instrumental, meant to insulate and investigate the demand-driven phenomena, and that it may be generalized by simply endogenizing the parameters used in this implementation of the model (see Valente, 2000, for one of the possible extensions of this model). We consider a market for potentially heterogeneous products that are “perfect” substitute in the eyes of consumers. That is, the demand side of the market is defined by the basin of users that accept as potential purchases all products available. In other terms, we do not consider buyers being differentiated a priori by constraints (e.g. different budgets) or special needs (e.g. different requirements), which may segment the market with exogenous elements. Rather, we will concentrate the analysis on the endogenous dynamics stemming from the interaction between supply and demand. In the following we discuss the main aspects of supply: product representation and role of marketing.

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See http://www.business.auc.dk/lsd for a simulation language, proposed by the author as part of the doctoral thesis, that aims at solving most of these problems. At http://www.business.auc.dk/~mv/Thesis/Thesis_header.html is available the model used here. For the specific configurations used in the paper contact the author.

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Product Representation The model considers products as represented by a vector of characteristics. This representation has been frequently proposed in the literature (Lancaster, 1966, Saviotti and Metcalfe, 1984, Gallouj and Weinstein, 1997) and is the most general way to represent a market for a heterogeneous product. Each product is therefore defined by one "measure" along each of the characteristics; examples may be the "cheapness" of the product, the maximum speed and consumption (for cars), disk capacity and computing speed (for computer). We assume in the model that the each characteristic is measured along "positive" values, so that the higher the characteristic the better for the consumers (e.g. we measure "cheapness" and not price level). This assumption is clearly not constraining, and may be easily removed, although complicating the implementation. However, given the highly abstract and general goals of this work, we will always maintain such hypothesis. Note that, given this representation, the notion of superiority of a product as compared to another cannot be determined objectively, but depends on subjective criteria, like the relative importance of each characteristic for consumers. It is worth to note that such general representation is very flexible, allowing, for example, to extend the simple model considered here by endogenizing one or more characteristics. For example, it may be possible to consider dimensions for price, brand attractiveness, specific quality measures, each subject to its own dynamics, under the producer’s control or depending on other elements. In the model presented below we will not attach any particular meaning to the product characteristics. Moreover, they will also be kept constant during the simulation exercises. This choice is due to allow an easy understanding of the model dynamics (originated in the demand side of the market). Marketing Firms do not only offer products, but are also engaged in marketing activities promoting their product. Modelling marketing is extremely difficult, reflecting partly the fact that its effects are unknown, frequently even to the actual firms implementing them. However, even a casual observation of any real world market reveals that the marketing is considered an extremely relevant activity. Modern consumption patterns are strongly influenced by the marketing strategies of firms, even though the eventual outcomes may be quite different from the desired ones. Frequently, marketing expenses are even higher than production expenses, and marketing strategies are becoming the really driving forces within companies. It is therefore worth to suggest a possible general modelization of how marketing activities affect demand's behaviour. We assume that marketing takes the form of "promotion of product's vision": producers try to convince consumers of a given perspective of the nature of the product, which implicitly fosters 4

their own product in respect of the competition. For example, one car producer may advertise cars are status symbols, another as a cheap transportation mean, and yet another as a tool for an exciting sport. In this example, the three producers want to enhance their sales by proposing visions that implicitly favour stylish, cheap or fast cars respectively. Although this proposed representation of marketing is highly simplistic, and possibly even incomplete, we think it captures most of the effect of marketing, at least to the degree of abstraction required for the exercises described below.

Modelling Consumers’ Behaviour The literature providing information on consumers' behaviour can be roughly grouped in three different strands. A first kind of works concerns the account that economic theory provides of consumers' behaviour, the most known of which is the standard consumers' theory in neoclassical economics. In this case, consumers are represented as perfectly rational agents who optimize their utility (or some related concept) given the market conditions and their personal preferences. Note that the assumption of rational behaviour cannot rely, as for the case of competing producers, on the "as if" hypothesis. In fact, while producers can be thought as subject to a selection process removing sub-optimal agents (i.e. competition), there is no reason to assume consumers as subject to a similar selection dynamics: sub-optimal consumers, whatever may mean, cannot be selected out of the market. Therefore, the only possibility for the theory to be confirmed relies on its validation by actual observations. Even though the validation is difficult because of the impossibility to observe directly consumers' preferences, a wide body of evidence shows that the basic axioms of the theory are systematically violated by people in experiments and real world cases. This evidence is collected in an increasing number of works concerning cognitive studies on human behaviour, and constitutes the second source of information on consumers' behaviour (e.g. Devetag 1999). Though it started as an attempt to account for the deviations from standard normative decision theory, it also contains works that explicitly refuse the standard rationality model even as reference point, suggesting positive models of human behaviour, based on the assumption of bounded rationality (Gigerenzer, 1997). The works cited above deal mainly with choices made by individuals with given preferences. The last source of information on consumers' behaviour is composed by the large amount of work done by marketing research. Given its applied nature, these works are less interested on providing a global coherent picture of consumers' behaviour, but provide a large number of examples on how firms can influence, if not determine, consumers' behaviour. Even though the first two kinds of works differ from the perspective of marketing researchers, it is possible to interpret the marketing 5

literature as suggesting that consumers' preferences are not exogenously given, at least in many relevant cases. That is, consumers' preferences are affected by the activities of producers aiming at promoting their products. This phenomenon can hardly be considered as not concerning economics, since it affects deeply the consumers' behaviour (and therefore demand) and stems from strategies of producers, along with their productive, technological, pricing etc., which are normally accepted to be part of economics' interests. Note that the influence of preference by means of marketing strategies is one factor along many others, like income and social composition of demand. Many recent studies has showed the importance of these factors (see, e.g. Cowan et al., 1997, Aversi et al., 1999). However, here we are interested in focusing on the factors internal to markets' only, while income and social dynamics are clearly exogenous to a single market. Therefore, considering the effects of producers' marketing activities and neglecting as exogenous the social structure of demand is only meant as a ceteris paribus experiment, to be potentially extended in the future. In summary, the conclusions that can be derived from the literature are the following: - the standard rational model of decision making, although normatively sound, fails to provide a realistic description of actual observations; - the bounded rational paradigm provides the most convincing interpretation of actual consumers' purchasing choices; - consumers' preferences used in purchasing choices are influenced (among many other factors) by purposeful strategies that producers implement in order to promote their products. In the following the we describe a proposal to model the choosing algorithm and the marketing effects on preferences. Choosing Among Alternatives The main problem in modelling consumers' behaviour is to devise an algorithm showing the characteristics of bounded rationality (Simon, 1952, 1982). The problem facing agents is, stated in very abstract and general terms, to choose which product to buy among a set of alternatives4. The algorithm here proposed is derived from the Gigerenzer’s proposal, (Gigerenzer, 1996), which explicitly refers to it as a proposal for representing of bounded rational agents’ behavior. It is referred to as Take-The-Best (TTB) strategy and it has a number of properties that support it as adequate for the representation of bounded rational decision-makers. In fact, it is showed to be very effective, in that it provides success rates equal or superior to many sophisticated decisional algorithms (bounded rational does not mean irrational…). It is very parsimonious in the use of 4

To simplify the analysis the model neglects the problem of forming the set of alternatives, the costs of research etc. However, this aspect is one of the possible extensions of the model, and may easily be included to study phenomena where these are relevant aspects.

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available information, limiting to explore only the part that can bring to a decision rather than using all the available information. It is “robust” in the sense that it is “forgiving” in case unreliable or missing information must be managed during the decisional process. The TTB strategy is based on the use of the lexicographic ordering of product characteristics. It consists in ranking the characteristics of the product according to their decreasing relevance for the buyer. Then, the most important characteristic is used to discriminate on available alternatives: products scoring less than the maximum are eliminated from the list of alternatives. If only one product is acknowledged as the best (according to the characteristic used), then this product is chosen, without further analysis. If more than one product is still a valid alternative (i.e. they are equivalent according to the “criterion” set by the highest-ranking characteristic), then the secondranking characteristic is used, and so on until only one alternative remains. In case all characteristics are used and more than product is still in the alternative list a random draw determines the final choice. The algorithm used is rather straightforward. It is centred on the ranking of the characteristics used by buyers, with each characteristic working as a "filter" removing some of the available alternatives. In this way it is possible to represent buyers as using the same algorithm and different rankings, producing very different results. In other terms, the ranking of characteristics defines the preferences used by a buyer. Learning As further elaboration on the basic TTB, the model used below considers two other aspects, assumed relevant for consumers' behaviour. Firstly, consumers are supposed to be subject to learning, expressed simply as the capacity of buyers to correctly "read" the value of considered product along the used characteristic. Agents with no prior experience can make large errors in estimating the actual value of a product, while expert buyers (high learning) are able to correctly read the values of products. The "errors" are expressed as the variance of the normal random variable (centered on the true value) from which the observation of buyers is made. Later, we will see how the learning level for each agent is determined. Tolerance The second variation of the basic TTB model is the "tolerance" effect. This is meant to compensate for the possible effects due to the (arbitrary) choice of the numerical representation of products' qualities. We saw that inferior products' are discarded by buyers, but this applies both in case of large and very small differences in products' qualities. As a matter of realism we introduced a parameter meant to represent the "tolerance range" within which a (not so much) inferior product 7

is considered equivalent to the best one. During the TTB process, when the buyer is comparing products' along one dimension, products' are discarded only if their difference with the maximum is larger than a given percentage. Note that this effect is different from learning, which is a stochastic error, while the tolerance is a deterministic range. Moreover, as we will see below, learning modifies through time while tolerance is a constant characteristic of the model. Preferences Formation As mentioned above the preferences are constituted by a ranking of product' qualities used to filter available alternatives until one single option is remained for purchase. To maintain the generality of the model we assume that buyers do not have a priori preferences5, but these are induced by producers' via marketing activities. That is, each producer assigns an "importance" weight to each dimension, hoping that the buyers' preferences will follow the same ranking. This represent the "vision" of the product that producers try to induce in buyers, and it is the typical case for radically new products, where buyers have scarce or not personal experience of the product. However, producers' marketing strategic decisions are not the only factors in determining the consumers' preferences. Moreover, it is likely that producer' vision are conflicting, since each producer will try to impose on demand a vision that favour its own product against the competition. The model assumes that, while buyers select the product to purchase using preferences, they "select" alternative preferences using a socially driven criterion. Although, as said, the model neglects the exogenous effects of social composition of demand per se, there is still a specific kind of social function that concerns the diffusion of marketing messages. The model adopted is inspired to a work by Smallwood and Conlisk, 1979 on the capacity of the markets to diffuse information on the quality of products. They convincingly argued that consumers derive information concerning (unobservable) properties of alternative products by looking at their market shares. In our case, the information carried by market shares does not concern directly the properties of products, which are assumed to be observable. Rather, it concerns the validity of alternative "visions" of the product embodied in the preferences' structure suggested in the producers’ marketing efforts. The higher a market share for a product, the "heavier" is the weight of the preferences suggested by that producer in the eyes of consumer. Note that in this framework the reliance of preferences on market share has a further justification, besides the arguments brought by Smallwood and Conlisk. The model implicitly represents the social value attached to purchasing: a consumer is pressed to adopt the preferences structure most popular among his fellow consumers. Further support to this implementation is provided considering that the very diffusion of a product is a very important

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medium for transmitting the producer's "vision" of the product. That is, the best marketing for a product is simply to have many items of the product be shown around by previous buyers who have chosen it. Summarising, preferences are defined as a ranking of product characteristics, and they constitute a certain "vision" of the product. Producers affect consumers' preferences by pushing them to give a high priority to given characteristics and low to others, with the purpose of enhance their own product. Consumers are subject to the marketing activities of each specific producer proportionally to the market shares of that producer. Implementation The algorithm implementing the formation of preferences is based on a sequence of random draws of characteristics, with the order of extraction used as actual ranking (i.e. first characteristic drawn is the top ranking one, the second drawn is the second ranking and so on). The probability of each characteristic to be chosen as the highest-ranking is computed as the average of the importance given by producers to that characteristic, weighted with their market shares. Consider the index i referring to m characteristics and the index j referring to n producers. Be rij the value of importance of characteristic i for producer j. That is, producers can stress the importance of one characteristic as compared to another by raising its r value for the characteristic they would like to be at the top level in buyers' preferences. Be sj the market share of producer j. The value n

(

f i = ∑ ri j s j j =1

)

δ

is the “raw” probability indicator for characteristic i. The value of stj can be 0, especially in the beginning of the simulation runs. To avoid obvious distortions, in these cases stj is substituted with a positive (very low) value, so that every producer contributes to the preferences’ formation. The interpretation is that firms, by means of their very existence, have the possibility to influence, though minimally, the behaviour of buyers, though most successful competitors have the largest influence. The actual probability is obtained normalising the fi’s :

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Or, equivalently, that every available product scores identically in respect of the a priori preferences, which therefore have no effect on buyers' behaviour.

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pi =

fi m

∑f

h

h =1

After having determined the most important characteristic, the value of fi for the chosen characteristic is set to zero, and the probabilities are re-computed using the same fi with a new normalization. Using these new probabilities consumers draw randomly the second ranking characteristic and, always setting to zero the values of drawn characteristics, continue until all characteristic have been assigned a ranking. The exponent δ in the computation of the “raw” probability indicators determines the “concentration” of the probabilities (see Smallwood and Conlisk, 1979). For δ close to zero, all the probabilities tend to be identical, and therefore the preferences of buyers will differ pretty much since they will randomly chose characteristics without any common criterion. In fact, different buyers will draw different characteristics, making the set of preferences highly varied. Instead, for δ close to infinite the highest probability approaches 1 and all the others are negligible. This means that the characteristic enjoying the highest "marketing value" for the producer with the highest market share will be the top ranking characteristic for every consumer, and this will repeat for all the other characteristics.

Model Dynamics It is well known that a simulation model, based on given algorithms and identical parameterization, is likely to produce very different results depending on the timing of activation of the different algorithms. Note that this is not a weakness of simulation methodology, but it is rather one of its strength. In fact, the importance of timing is a well known fact in the real world economic events, which is simply eliminated by most of economic theory. It is therefore important to describe a simulation model not only by mean of the single routines implemented, but also on the timing of their activation. Before such description it is worth to repeat that the supply side of the market is kept constant throughout all the simulation runs described in the following section. Of course, this assumption is far from realistic, and, and this grounds, it may be criticised when compared with the high degree of detail used to describe buyers’ behaviour. Of course, the model may be successfully extended to include more realistic supply’s representations (see Valente, 2000, and the concluding section below). However, the simulation exercises described here do not aim at providing realistic results, but rather at allowing a clear understanding of the aggregated phenomena considered. It is therefore the choice for clarity that pushes for a unrealistic, but easy to investigate, representation of supply side of the market,.

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Buyers' Entry The model assumes that the buyers' enter gradually in the market, as is the case for markets of innovative products. The model represents the typical s-shaped dynamics of the number of buyers in the market; this is not assumed exogenously, but is obtained as result of the peer communication among a social community (see Valente, 2000, for a description of the algorithm used). Basically the entry mechanism represents a "contagion" model where an initial small number of users introduces a new product to their circle of friends, which slowly decide to buy themselves the new product. A new buyer, in turn, will introduce the new product to his own circle of friends, bringing in the market a number of new buyers which depends on the amount of people do already entered in contact with it. The initial exponential rate of entry is in time slowed down by the approaching of the saturation level, where the number of individual who are still unaware of the new product decreases exponentially. This mechanism to represent the expansion of the demand for a product is of importance because, as we will see below, it influences the distribution of knowledge on the product and the formation of preferences. However, it is worth stressing that it is also a first step of a phenomenon that, although not developed in the present stage of the analysis, is one of its most interesting extensions. That is, the formation of classes of buyers that, entering at the same stage of the market, or being connected to the particular users, exchange information on the product in a different way that with the rest of demand. Purchasing timing The model assumes that buyers perform the purchase of a product one every basic time steps of the simulation. That is, the model represents a market for a semi-durable product, which must be replaced from time to time. The interval between two purchases is a random variable drawn from a uniform function. Consequently, the market can be measured at each time step along two quantitative dimensions: number of users who own a product, or the number of products bought at that time step. In the first case we refer to installed base, while in the second to sales; both measures can be computed for the whole market, for each single producer, and made relative to compute market shares. Obviously, the number of sales in each period is a fraction of installed base, whose amount depends on the expected value of the random function determining the interval between two purchases. Note that the model can be stretched to consider non-durable goods (upper bound of the interval set to 1) or one-time purchases (lower bound of the interval set to ∞).

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Preferences Formation The results discussed below consider that buyers set their preferences once and for all at time of their very first purchase. This is a rather extreme simplification representing rather "stubborn" buyers who are not influenced by marketing after they start to be users of the product. This simplifying assumption states that buyers' preferences reflect the social information on the product as available at the time when they made the first decision without having never owned an instance of the product before. Instead, when buyers replace the current product with a new one, their preferences are not modified. This assumption can be more or less realistic depending on the type of the product considered. However, here is meant to be a simplification aimed at interpreting more easily the results. See Valente, 2000, for an extension where buyers are allowed to modify their preferences even after their first purchase Learning As mentioned above, buyers are subject to a learning mechanism whose effect, concerning the model analysis, is that they become more and more expert in choosing during subsequent purchases. We saw that when buyers have to decide which product to buy they compare products' quality level along one of the dimensions. However, the model assumes that the generic buyer j at time t do not observe the true values of products Vi (where i is one of the characteristics), but a draw from a normal random function:

(

ViObserved = Normal Vi , σ t j

)

The distribution is centred on the "true" value of the quality of the product, while the variance is a function of the learning cumulated by the agent. To simplify, the learning dynamics is represented by a constantly decreasing σ from one initial (maximum) level when the agent firstly buy one product and decreases up to a minimum level, determined by a parameter. The decrement is just due to the passage of time, assuming that buyers develop individually the skills to judge the value of a product while using it. If the minimum level of σ is set to 0, then the model represents agents that can develop "perfect" learning, since in the long term they can perfectly judge products' qualities. Instead, if the minimum level is positive, the model represents' the case where even in the long term buyers continue to make (small) mistakes when reading the value or products' characteristics. In summary, a simulation run contains the following dynamics: - buyers enter in the market for a new product following a s-shaped diffusion pattern, rooted on the social diffusion of the awareness of availability to a new type of product; 12

- at time of entering the market (i.e. when making their first purchase) buyers determine their preferences, which are a function of the marketing strategies of producers and the current distribution of market shares; - after the entry, from time to time buyers replace their product with a new one, chosen with the TTB strategy applying the initially determined preferences; - since a buyer enters in the market, his learning permits to decrease the errors made when judging products' qualities. One of the goals of this work is to underline some of the components of market dynamics that are usually neglected in economic theory. The above description of the model's dynamics is therefore rather incomplete, if judged in terms of realism, but underlines few aspects: - there are several demand dynamics that take place along different time scales: entry of buyers in a new market, preferences formation (and modification), actual purchases, learning. The properties of such dynamics do influence, and are influenced by the conditions on the market; - preferences are "formed socially"; at least partly, most product making up modern economies markets' have their intrinsic value determined by the result of the social elaboration of marketingdriven information emitted by producers; - purchasing is a bounded rational activity, because of lack of information and lack of tools to elaborate other more sophisticated strategies. Moreover, in most relevant cases, buyers have no strong incentives or selection pressure to behave differently, even when "optimal" or rational purchasing behaviour may be assigned a meaning; The model proposed, even in its simple descriptive formulation, provide an occasion to think about the relevant components of demand. In the following, we present the results obtained with few particular configurations of the model. Again, it is worth repeating that the aim is not to provide realistic representation of any observed dynamics, but to perform some "thought experiments" in order to assess the effects of some assumptions.

Simulating the Model The simulation exercises discussed below are meant to show that, even with such a simplified system as the model presented above, is possible to obtain a varied number of market configurations. More than simply replicating realistically some phenomena, the analysis of the simulations will permit to find the link between characteristics of the market (stated in the model assumptions) and eventual observed dynamics. That is, the relevance of performing these exercises is that we are able to link the aggregate properties observed in the simulations with the micro "causes" underlining our assumptions. It is therefore obvious that this is not a "mathematical" 13

model, on which we have to explore the whole parameters' space in order to assess the robustness of some general property. Rather, we want to "discover" in the simplified, simulated toy world represented in the model, some causal link, as inspiration for what is actually going on, together with many other events, in generally interesting markets. The model represents a fixed number of producers each supplying one single differentiated good. We assume that the goods are perfect substitute; that is, the consumers considered may choose any one of the products, if were not for their personal preferences6. The model assumes that products and producers’ marketing strategies do not change through the simulation exercise. This assumption is used to permit a clear understanding of the model dynamics. The parameters for supply side that we will consider as relevant in the simulation are the following: - marketing strategies of producers; these are represented as the vectors (one value for each characteristics) of weights that the producer would prefer buyers use as preferences; - products' object qualities; a vector of values (one for each characteristics) expressing the positive values of the product along product's dimensions; Demand is represented by a fixed number of buyers, entering in the market with the dynamics described above. Each consumer applies identical strategies and uses identical parameters, so that their differences can depend only on random reasons and on the state of the market when their decisions are taken. The relevant parameter considered are: - δ; this parameter expresses the "trust" of buyers in respect of the information coming from the market share distribution. A very high δ means that buyers rely their preferences completely on the marketing strategies of the producer that sold most7. A very low δ expresses a high variability in the distribution of preferences, in that buyers will "shop around" randomly their preferences across all the producers, despite their relative market performance. - limit learning; all buyers start with very low capacity to judge product's qualities, causing them to make large mistakes when choosing which product to buy. They have the same learning dynamics that through time brings them to narrow their errors in reading products' qualities. If limit learning is very high, the error goes to 0 and buyers are able to read perfectly the true products' qualities. If limit learning is low, buyers continue forever to make (relatively small) errors in judging products' qualities. - tolerance; this parameter expresses the range of equivalence of products' qualities. No tolerance means that the even slightly lower quality level than the maximum justifies for a buyer to eliminate

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In other terms, the products, though differentiated, provide similar functions within the same range of prices. The market shares used are referred to the installed base, which are a multiple of "daily" sales. Therefore, to have high market shares for installed base it is necessary to have sold more than competitor in the recent past. 7

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a product from its list of alternative potential purchases. Positive tolerance level means that if a product scores within a given range of quality in respect of the best product, they are considered equivalent and the choice between the two is decided using the next quality dimension in the buyer's preferences. For all the model configurations we will consider below we assume the following common aspects: - entry dynamics and total number of consumers; the models start assuming one single consumer is using the product (setting the preferences and choosing the product as described above). This early consumer will "introduce" to the new product 6 new consumers, which in turn will bring in the market 5 other consumers, and so on, until reaching a total of 1957 consumers. In Figure 1 is reported the plot of the number of consumers currently present in the market. Note that the number of actual purchases is always a fraction of such number, since only some of the current consumers do actually buy one product at each time step. - number of producers; 10 producers will compete on the market, each offering a product whose characteristics (qualities and marketing) are determined in the beginning and never change through the simulation. Pure Monopoly In order to get accustomed with the model basic functioning we present an early limit case configuration. We consider that all producers have identical "visions" of the product, promoting the same marketing strategies. This fact, associated with very high value for δ, ensures that each consumer will have identical preferences. Moreover, the configuration determines an absolute best choice: in respect of the first product characteristic (the top ranking in all consumers' preferences), one product is better than any other, being therefore the “natural” monopolist. In this circumstances, there is no question on the final state of the market: the best product will be chosen by everybody, and all other producers will have null market shares. However, before reaching this point there is the phase of "learning" during which just entered consumers are not able to apply correctly their (common) preferences. This extreme configuration assumes also that consumers will eventually reach the level of being perfectly able to judge product characteristics, and that there is no tolerance allowed for even slight differences in (perceived) quality levels. Summarising, the configuration assumes: - very high δ; - identical marketing strategies for all producers; 15

- one single superior product; - perfect final learning; - no tolerance The result is shown in Figure 2, where the absolute number of consumers using each of the products is reported. As expected, the final state of the market is a monopoly where the superior product sells to all consumers. This is due to the fact that all the producers' marketing strategies suggest the same preferences, and therefore consumers adopt it. All producers have identical qualities along each dimension, but for the first producer, whose product enjoys slightly better quality than competitors' on the first dimension. Since there is no tolerance, when consumers develop enough skills to appreciate the first product's superiority they choose it with certainty. However predictable, the final state is reached after a period in which all products enjoys identical patterns. Each product is chosen with positive probability because the consumers' ability to discern quality differences is very low. This results in random choices, centred on the (identical) true qualities of products, and therefore each producer sees its market shares growing thanks to the entry of new (i.e. unable to detect qualities with precision) consumers. Monopoly with Limited Learning As second exercise about this simple configuration of the model we report the result of a simulation identical to the first exercise above, setting a less than perfect limit learning. That is, consumers start with very poor capacity to judge products' qualities, and increase it with the time they own an item of the product, as before. However, even in the limit they do not reach the perfect capacity to read exactly products' quality, but will remain with a (small) error. In this case, as shown in Figure 4, the superior product is not able to exploit its advantage fully: a percentage of consumer will continue to fail to appreciate its higher quality and will choose another product. However, the superior product will enjoy higher-than-average shares, because (constantly mistaken) consumers will be biased to choose it against competitors. In this case, the monopolist’s power is reduced by the diminished capacity of consumers to appreciate its superiority. Monopoly with Quality Tolerance The goal of this last initial exercise on a monopoly set-up is to show the effect of the tolerance parameter. As said, tolerance allows inferior products to not be discarded if the quality difference is small, therefore postponing the choice to the subsequent quality in the consumer's preferences. The limit learning level is still allowed to be perfect in the event, meaning that buyers are perfectly able to read the true products' qualities. All the other parameterisations are left identical as before, in particular all products' qualities are identical. 16

In Figure 3 are reported the installed base values. This time the final state of the model is of a sharing of the market among each producer. In fact, the existence of tolerance removes the advantage of the first producer (we allowed for tolerance to be larger than the quality advantage of the monopolist). Since all products' qualities are identical, the choice is eventually made random. However, the pattern initially resembled the one as in the previous configuration: similar growth pattern for all producers, until the first one dominates the market. Instead, in this situation this pattern is reversed, until the may-be dominant producer's share becomes identical to the others. The reason is that, as long as there are consumers with a less then perfect capacity to judge products' qualities, the superior product enjoys higher shares since the “erroneous” readings of consumers are based on a higher mean value. This advantage is eliminated when perfect learning makes this advantage small enough to fall within the range of the tolerance level. At this point, consumers see the true, small, quality difference of that producer, and neglect it, passing to use the second, third and so on quality trying to decide which one to buy. Since no dimension allow them to choose, they make a purely random choice. As seen, this is a counter-intuitive case where improving learning favours the superior product up to a certain time. After that, the superior product suffers from the very precise capacity of buyers to "read" the true products' qualities, since they can acknowledge that the difference is, after all, not that relevant to be decisive, and move on to use the next product dimension as decisional criterion. In a situation like this, where the “superior” product is identical to the others but for one, not decisive, characteristics, obviously the market is evenly shared among all competitors. Pure Oligopoly As opposed to the “natural” monopoly considered above, the next exercise implements a sort of “perfect” oligopoly. That is, each firm is superior to the competitors in respect to one of the dimensions, and direct coherently their marketing efforts. That is, they try to convince consumers to adopt the dimensions on which they have a relative superiority as the most important in their preferences. Contrary to the exercises shown previously, this time consumers do not develop identical preferences: according to the distribution of market shares at the time when they enter in the market, they follow one or another “vision” proposed by a producer. Given a preferences settings, there exists in the market an optimal choice (each firm is better than others on one dimensions). Under this set up no producer has an a priori advantage in respect of competitors, but it is very likely that a self-reinforcing mechanism will increase the attractiveness of producers that, by chance, enjoy higher shares in the early stages of the market. That is, early (almost purely random) choices make shares fluctuate. Since preferences of new entrants depend on market shares, 17

once a producer takes a lead, it will be more likely to impose its own vision of the product, further increasing its leadership. In Figure 5 is reported a run under this set up, showing the self-reinforcing mechanism at work. Although it is not possible to forecast which producer will eventually lead the market, it is possible to know the eventual concentration. In fact, the higher the trust of buyers in the messages coming from the market (parameter δ), the stronger will be the concentration index. Elsewhere (Valente, 2000) it has been reported the average concentration markets for different values of δ. The inverse herfindal index (that is, the number of firms with identical market shares that would produce an identical concentration) ranges from 10 for δ equal to 1, up to 1 for δ larger than 3. “Random” Oligopoly All the previous exercises have been based on very specific configurations for supply. This has permitted to observe and understand clearly the results produced. In this latter series of exercises we will use a more chaotic configurations. Firms are assigned random levels for both products’ qualities and marketing strategies. For the same random configuration of supply we will apply different parameterizations of demand, exploiting the insights gained earlier to provide a rationale for the results. As first case, consider the model where consumers have a medium level of trust in the market, are allowed perfect learning and have no tolerance. We will compare this result with three other setups, summarised below: Figure

Limit Learning

Tolerance

Figure 6

Perfect

No tolerance

Figure 7

Perfect

Positive Tolerance

Figure 8

Limited

No Tolerance

Figure 9

Limited

Positive Tolerance

As it shown in Figure 6, some of the producers can enjoy positive market shares only as long as there are consumers with poor capacities to judge products. When all buyers develop a perfect capacity to judge products, they are doomed to disappear from the market, meaning that they are absolute inferior, whatever the preferences of consumers. The remaining producers will distribute their market shares in a path-dependent format. In the event, when all consumers develop perfect learning, the market share stabilize, since each consumer will shop only from the producer most adapt for its preferences.

18

In the second exercise we have introduced some positive tolerance. The picture changes substantially, even though the supply configuration did not change. The most striking aspect is that some of the previously surviving firms do disappear, while other that before were forced out of the market, in this case survive. The reason is that without tolerance products slightly superior on one dimension and very bad in all the others can still win the market, while with positive tolerance this “narrowly focused” advantage disappears. Another aspect is that there is a small variability in market shares even in the limit, although robustly centered on clearly determined average values. This is due to the fact that part of consumers develop preferences that allow them to identify clearly a most preferred product, and consistently buy it. But there is another group that, in the course of choices, cannot identify a best product, and eventually choose randomly. In other terms, the market is formed, as before, by a clearly segmented group of consumers, and by another group that shops around randomly. In the third exercise we allow for only a limited learning, and no tolerance. This set up allow every firm to enjoy positive market shares, even the clearly inferior ones, due to the errors that buyers continuously make in reading products quality. The ranking of (average values for) producers resembles roughly the one seen in the first exercise, although less concentrated and with some interesting aspects. One of these is that firms due to disappear when perfect learning were allowed now they are relatively prominent in the market. It means that it is at work a mechanism similar to the effects of tolerance. That is, inferior products are doomed to disappear in a perfect learning world. But if these products are only slightly inferior on many different dimensions of the product, they can still enjoys the choices of “mistaken” buyers with many different types of preferences. As last exercise we allow for, both, positive tolerance and limited learning (Figure 9). The results resembles the ones shown in Figure 7, although less clearly marked. The dominant feature seems to be the existence of positive tolerance, favouring not so much the highest quality products (in one dimension), but the “robust” products, which score reasonably well in many dimensions. The role of learning seems that of introducing some random fluctuations reduce the differences among producers.

Conclusions and further research This work proposes to stress the role of demand in the economic analysis, as it is increasingly suggested in much of the recent literature. Normally, the attention of researchers concentrates on the exogenous phenomena affecting demand. Typically, it is discussed the influence of social factors, or the psychological determinants of consumers’ behaviour. Of course, distribution of social classes, preferences and capacity to judge effectively among alternative choices are considered as 19

exogenous determinants of the economic dynamics. In this work, instead, we have discussed that part of demand’s behaviour that is under the influence of purely economic events. We have allowed for very general and loose assumptions: -

we considered a market for multi-dimensional, differentiated product;

-

we assumed buyers entering in a market with no a priori preferences or constraints

-

buyers construct their preferences as a function of the market configuration

-

given preferences, buyers apply a bounded rational decisional algorithm

The model is relatively simple in its basic elements: -

a set of constant products is available for purchase;

-

buyers enter gradually in the market as the knowledge of a new product diffuses through the society;

-

buyers apply the Take-The-Best decisional algorithm (lexicographic preferences)

The most innovative elements in the model is the explicit consideration of the role of marketing, by far the most neglected aspect in economic theory notwithstanding is enormous, and increasing, relevance in practically every modern market. By marketing is meant the pressure that suppliers apply trying to have consumers to adopt a certain “vision” of the product. This vision is clearly connected to the preferences that are then applied to choose the product to buy. We have analysed the results of several configurations aiming not at the realistic reproduction of observations, but at the attempt to explain the emergence of the simulated aggregate configurations. We have seen the importance, and the mechanisms of influence, of three main factors: -

trust of buyers in the information gained at aggregate level (market shares distribution affecting preferences)

-

capacity of buyers to correctly judge the technical content of differentiated products (how far learning by using allow a correct technical judgment)

-

existence of tolerance in respect of small differences in products’ qualities (how important are quality differences)

The main results are that we can produce explanations of simulated patterns in terms that clearly understandable to every observer of real world events, in particular relating the “objective” quality levels of products, the marketing strategies adopted by producers and the overall demand attitudes, related to the nature of the product. We have seen that rather simple set-ups turn to produce highly unexpected results when even a slightly different parameterization is applied. More than the actual numerical values produced, the advantage of the modelling methodology adopted is that we can “tell the story” on what has happened, and why, in the simulated toy world. 20

However interesting these early experiments, the model proposed should be mainly considered as a robust building block for more realistic experiments. For example, the same model of demand has been integrated with an evolutionary economics type of supply side of a market to study the relation between technological innovation and competitive structure (Valente, 2000). However, many other extensions of the model may be considered. For example, it may be possible to remove the (hardly realistic) assumption of totally identical buyers, introducing the effects due to a stratified society, where consumers have differentiated behavioural attitudes. This may be done by simply moving the parameters determining consumers’ behaviour from the aggregate entities (being identical for everybody) to the individual consumer’s entity (differentiated). Moreover, the model provide explicitly the “social chain” through which information about a product is passed. This may easily be exploited in assuming that newly entered buyers pay more attention to the people who are more closely related to them, rather than, as it is now, at the market as a whole. The model may also be used to test the effectiveness different marketing strategies given the nature of available competing products. As such, this may be a valuable instrument in the notoriously difficult exercise of assessing the complex effects of marketing. The model may help in finding out when is better to, for example, provide detailed information on producers’ own product, or when it is better to present the product as similar to the others. Another possible use of extensions of the present model is to determine the possibility for a public actor to improve the overall welfare for consumers by regulating the information on available products and their actual technical values. This is a clearly relevant aspect in the debate over the role of public institutions in setting technical standards. The main goal of this work, however judging the value of the model, is to call for re-balance the economic analysis in giving demand the importance it deserves as necessary component of any market. This work invites to consider that, even though many exogenous (i.e. non economic) elements affect the demand, there are also many aspects that are under the direct control of individual or aggregate economic entities, and therefore fall within the domain of economics.

References Aversi, R., G. Dosi, G. Fagiolo, M. Meacci, C. Olivetti, 1999, “Demand Dynamics With Socially Evolving Preferences”, Industrial and Corporate Change. Cowan,R., Cowan,W. and Swann,P. ,1997 , “A Model of Demand with Interaction among Consumers”, International Journal of Industrial Organization, 15, 711-732. Gallouj, F. and Weinstein, O., 1997, “Innovation in Services”, Research Policy, 26. 21

Gigerenzer, G., 1991, “How to Make Cognitive Illusions Disappear: Beyond Heuristics And Biases”, European Review of Social Psychology, 2, 83-115. Gigerenzer, G. 1996. Rationality: Why social context matters In P. B. Baltes & U. M. Staudinger (Eds.), Interactive minds: Life-span perspectives on the social foundation of cognition (pp. 319-346). Cambridge, UK: Cambridge University Press. Gigerenzer, G., 1997, “Bounded Rationality: Models of Fast and Frugal Inference”, Swiss Journal of Economics and Statistics, vol.133, n.2. Gigerenzer, G. and Goldstein, D.G., 1996, “Reasoning the Fast and Frugal Way: Models of Bounded Rationality”, Psychological Review, vol.103, n.4, 650-669. Devetag, M.G., 1999, ”From Utilities to Mental Models: A Critical Survey on Decision Rules and Cognition in Consumer Choices”, Industrial and Corporate Change. Lancaster, R., 1966, “A New Approach to Consumer Theory”, Journal of Political Economy, 14. Metcalfe, J.S., 1998, “Consumption, Preferences and the Evolutionary Agenda ”, CRIC Discussion Paper 20, Manchester. Saviotti, P.P. and Metcalfe, J.S.1984, “A Theoretical Approach to the Construction of Technological Output Indicators”, Research Policy, 13. Simon, H.A., 1955, “A Behavioural Model of Rational Choice”, Quarterly Journal of Economics, 69, p.99-118. Simon, H.A., 1982, Models of Bounded Rationality, Cambridge, MIT Press. Simon, H.A., 1990, “Invariants of Human Behavior”, Annual Review of Psychology, 41, 1-19. Smallwood and Conlisk, 1979, “Product Quality in Markets where Consumers are Imperfectly Informed”, Quarterly Journal of Economics, XCIII, 1, p. 1-23. Valente, M., 2000, Evolutionary Economics and Computer Simulations - A Model for the Evolution of Markets, Doctoral thesis, University of Aalborg, Denmark. Veblen, T., 1899, The Theory of the Leisure Class: an Economic Study of Institutions, New York, MacMillan.

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Appendix - Figures Figure 1 - Number of Consumers in the Market 1976.56

1482.67

988.78

494.89

1 1

63

125

187

250

TotAgent_1

Figure 2 - Installed Bases for Monopoly 1 350.47

262.853

175.235

87.6175

0 1 InstallBase_1_1 InstallBase_1_7

200 InstallBase_1_2 InstallBase_1_8

400 InstallBase_1_3 InstallBase_1_9

InstallBase_1_4 InstallBase_1_10

600 InstallBase_1_5

800 InstallBase_1_6

23

Figure 3 – Monopoly with tolerance on small quality differences 594.89

446.168

297.445

148.722

0 1 InstallBase_1_1 InstallBase_1_7

200 InstallBase_1_2 InstallBase_1_8

400 InstallBase_1_3 InstallBase_1_9

InstallBase_1_4 InstallBase_1_10

600 InstallBase_1_5

800 InstallBase_1_6

Figure 4 – Monopoly with limited maximum learning 350.47

262.853

175.235

87.6175

0 1 InstallBase_1_1 InstallBase_1_7

200 InstallBase_1_2 InstallBase_1_8

400 InstallBase_1_3 InstallBase_1_9

InstallBase_1_4 InstallBase_1_10

600 InstallBase_1_5

800 InstallBase_1_6

24

Figure 5 – Natural Oligopoly with perfect learning and no tolerance 735.28

551.46

367.64

183.82

0 1 InstallBase_1_1 InstallBase_1_7

100 InstallBase_1_2 InstallBase_1_8

200 InstallBase_1_3 InstallBase_1_9

InstallBase_1_4 InstallBase_1_10

300 InstallBase_1_5

400 InstallBase_1_6

Figure 6 – Random Oligopoly with perfect learning and no tolerance 594.89

446.168

297.445

148.722

0 1 InstallBase_1_1 InstallBase_1_7

150 InstallBase_1_2 InstallBase_1_8

300 InstallBase_1_3 InstallBase_1_9

InstallBase_1_4 InstallBase_1_10

450 InstallBase_1_5

600 InstallBase_1_6

25

Figure 7 – Random Oligopoly with perfect learning and positive tolerance 1219.07

914.303

609.535

304.767

0 1 InstallBase_1_1 InstallBase_1_7

150 InstallBase_1_2 InstallBase_1_8

300 InstallBase_1_3 InstallBase_1_9

InstallBase_1_4 InstallBase_1_10

450 InstallBase_1_5

600 InstallBase_1_6

Figure 8 – Random Oligopoly with imperfect learning and no tolerance 378.75

284.062

189.375

94.6875

0 1 InstallBase_1_1 InstallBase_1_7

150 InstallBase_1_2 InstallBase_1_8

300 InstallBase_1_3 InstallBase_1_9

InstallBase_1_4 InstallBase_1_10

450 InstallBase_1_5

600 InstallBase_1_6

26

Figure 9 – Random Oligopoly with imperfect learning and positive tolerance 780.73

585.548

390.365

195.183

0 1 InstallBase_1_1 InstallBase_1_7

150 InstallBase_1_2 InstallBase_1_8

300 InstallBase_1_3 InstallBase_1_9

InstallBase_1_4 InstallBase_1_10

450 InstallBase_1_5

600 InstallBase_1_6

27