boundedly rational consumers · two product in respect of one single characteristic, v∗x i and v...

Model for consumers Simulation results Conclusions

Boundedly Rational Consumers

Marco VALENTE1

1LEM, S. Anna School of Advanced Studies, Pisa

University of L’Aquila


Background

Mainstream : consumers’ behaviour is represented bymaximisation of a utility function whose parameters depend onun-observable personal preferences. Many criticisms can beraised against this perspective.


Background


Evidence against rationality among consumers, and lack of“competitive” pressure necessary for the as if argument.


Background


Evidence against rationality among consumers, and lack of“competitive” pressure necessary for the as if argument.Firms’ successes and failures depends on demand, andtheir explanations must ultimately lie in consumers’behaviour.


Background


Evidence against rationality among consumers, and lack of“competitive” pressure necessary for the as if argument.Firms’ successes and failures depends on demand, andtheir explanations must ultimately lie in consumers’behaviour.Empirical evidence shows that demand is heavily affectedby market conditions, and firms actively engage in (tryingto) shape their own demand.


Background


Evidence against rationality among consumers, and lack of“competitive” pressure necessary for the as if argument.Firms’ successes and failures depends on demand, andtheir explanations must ultimately lie in consumers’behaviour.Empirical evidence shows that demand is heavily affectedby market conditions, and firms actively engage in (tryingto) shape their own demand.Theoretical requirements: explanation of changing marketconditions are necessary to explain the evolution ofmarkets, and depend on consumers’ behaviour.


Outline

Goal : understand how consumers behaviour affect markets’configurations.


Outline


Design of a model of consumers’ behaviour: simple,flexible and “realistic”.


Outline


Design of a model of consumers’ behaviour: simple,flexible and “realistic”.

Test the model under different assumptions on supply anddemand.


Assumption 1: Heterogeneous product/service

We define the products on the market as defined in terms oftheir evaluation in respect of m dimensions Xi , eachrepresenting one of many “qualities” relevant to buyers. Eachproduct is then represented by a vector of values:

Xm X2 ... Xm

Prod. A v1A v2

A ... vmA

Prod. B v1B v2

B ... vmB

... ... ... ... ...Prod. N v1

N v2N ... vm

N

Table: Products’ quality values



Note that we consider the price as any other characteristic(s),since this how consumers use the price (cost, proxy for quality,index of status, etc.).



Note that we consider the price as any other characteristic(s),since this how consumers use the price (cost, proxy for quality,index of status, etc.).

We also assume that consumers are identical in terms ofincome, technical abilities, possibility of access, or any otherother aspect not explicitly considered within the model.



We assume that consumers may make errors in observing thevalues of their product. These error are impredictable, andevenly distributed in the probability of over- or under-estimatinga product.



We assume that consumers may make errors in observing thevalues of their product. These error are impredictable, andevenly distributed in the probability of over- or under-estimatinga product.Instead of the true v i

X ’s consumers observe random draws froma normally distributed random function centered on the realvalue:

v∗iX = Norm(v i

X ,∆),

where ∆ is the measure of the (inverse) experience ofconsumers in evaluating products.


Observed values’ distribution function


Tolerance to errors and approximations

As we will see the model is based on the direct comparison oftwo product in respect of one single characteristic, v∗x

i and v∗xj .

We need to be able to assert whether i is superior, inferior orequivalent to j in respect of characteristic x .


Tolerance to errors and approximations

As we will see the model is based on the direct comparison oftwo product in respect of one single characteristic, v∗x

i and v∗xj .

We need to be able to assert whether i is superior, inferior orequivalent to j in respect of characteristic x .

Two products are defined as equivalent in respect of acharacteristic if their difference is below a certain threshold:

v∗xi ≈ v∗x

j ⇐⇒|v∗x

i − v∗xj |

v∗xMax

< τ


Assumption 2: Bounded rational consumers

To represent consumers’ behaviour we adopt the algorithmTake-The-Best (TTB), as proposed by Gigerenzer and hisgroup at MPI in Berlin.




TTB is shown to replicate very closely both weaknessesand strengths of people actual decisions in everydaychoices;




TTB is shown to replicate very closely both weaknessesand strengths of people actual decisions in everydaychoices;

TTB came out as good at least as good in competing atartificial problems with far more sophisticated (andcomplex) decisional algorithms.



TTB reminds an operationalized version of lexicographicpreferences:

1 Define: O the set of all products on offer; I the set of all thecharacteristics i defining the products.





2 Choose a characteristic i ∈ I.





2 Choose a characteristic i ∈ I.3 Remove from O all products scoring less than optimally in

respect of i .






respect of i .4 Set I = I − i .






respect of i .4 Set I = I − i .5 If I = 0 choose randomly a product in O.






respect of i .4 Set I = I − i .5 If I = 0 choose randomly a product in O.6 If |O| = 1 choose the only product left .






respect of i .4 Set I = I − i .5 If I = 0 choose randomly a product in O.6 If |O| = 1 choose the only product left .7 Return to 2



As an example, consider a product category defined over threedimensions: price, robustness and design. A consumer maychoose firstly to ignore all products appearing as not robust.Among these he may choose the cheapest and, among the fewremaining ones, eventually select the best looking one.



As an example, consider a product category defined over threedimensions: price, robustness and design. A consumer maychoose firstly to ignore all products appearing as not robust.Among these he may choose the cheapest and, among the fewremaining ones, eventually select the best looking one.

Though extremely simple, the TTB is very flexible and easilyextendible. Moreover, it applies to any kind of variable,requiring only the capacity to identify a product as equivalent tothe best on a certain dimension, or as dominated.


Assumption 3: defining preferences

Obviously, the results of the application of the TTB to the sameset of products would differ depending on the order in which theselecting dimensions are used. This is an opportunity for amuch needed definition: what exactly are preferences?



Obviously, the results of the application of the TTB to the sameset of products would differ depending on the order in which theselecting dimensions are used. This is an opportunity for amuch needed definition: what exactly are preferences?

It is common to refer to “preferences” as the explanation of agiven consumer’s choice. However, preferences are not thevery choice, but the criteria guiding the decisional procedure,which eventually produced the choice. For example, you mayhave two consumers with different preferences (criteria)choosing the same product, but for different reasons.



We can therefore define preferences in a precise way:

Preferences are the relative order of the product characteristics,for descending importance, as used in decisional processes

Market research companies routinely collect and exploit thisinformation.


Assumption 4: origin of preferences

Given this definition of preferences we can identify one of thesources influencing them (besides exogenous factors). Firmsacross countries, time and sectors spend huge resources inmarketing, signifying that they (hope to) influence consumers’choices. How does marketing works?



Given this definition of preferences we can identify one of thesources influencing them (besides exogenous factors). Firmsacross countries, time and sectors spend huge resources inmarketing, signifying that they (hope to) influence consumers’choices. How does marketing works?

Besides obvious effects (e.g. let consumers know that productX exist), we can assume that firms point to modify the criteriaused by consumers in order to favour their own product againstcompetitors.



We assume that firms attempt to modify the relative order ofimportance of the product characteristic. In the model we canthen define the desired preferences’ profile by each firm, interms of weights for each characteristic:

Xm X2 ... Xm

Prod. A k1A k2

A ... kmA

Prod. B k1B k2

B ... kmB

... ... ... ... ...Prod. N k1

N k2N ... km

N

where k iX is the importance of characteristic i that firm X would

like consumers to have.



We can expect that firms transmit contrasting messages, with afirm, for example, indicating that characteristic i is not relevantat all, while a competitor claims it must be the most important.How consumers form their own preferences?



We can expect that firms transmit contrasting messages, with afirm, for example, indicating that characteristic i is not relevantat all, while a competitor claims it must be the most important.How consumers form their own preferences?

Besides cultural, income, and other factors, we can exploit thestrong evidence that consumers’ tend to follow a “herd”behaviour, replicating what they see from their peers. However,consumers cannot observe directly preferences, but theresulting choices.



In the model we represent the origin of preferences assumingthat each consumer, when entering the market, decides his/herpreferences by weighting the messages from firms with theobserved market shares on the market.



In the model we represent the origin of preferences assumingthat each consumer, when entering the market, decides his/herpreferences by weighting the messages from firms with theobserved market shares on the market.Technically, the model builds for the consumer the followingindicator:

pi =

n∑

j=1

(k ij sj)

δ

where sj represent the market shares of supplier j , k ij is the

marketing level of firm j in respect of characteristic i , n is thenumber of firms, and δ is a coefficient flattening or steepeningthe indicators.



The indicators (normalized) are then used as probabilities toextract the first (the most relevant) characteristic, topping theconsumer’s preferences, and then all others are drawn in thesame way.



The indicators (normalized) are then used as probabilities toextract the first (the most relevant) characteristic, topping theconsumer’s preferences, and then all others are drawn in thesame way.

As a result, a characteristic strongly supported by thebest-selling firm is likely to come out at the top of consumers’preferences, while characteristics considered not relevant willfall in the end of the consumers’ decisional process.


Summary of assumptions

The model allows for:

1 Heterogeneous products/services, defined over multipleand diverse characteristics.





2 Consumers’ errors and approximations.





2 Consumers’ errors and approximations.3 Bounded-rational consumers’ decisions.





2 Consumers’ errors and approximations.3 Bounded-rational consumers’ decisions.4 Definition and some source of preferences.


Demand surfaces

The model is able to generate aggregate demand respectingthe basic tenets of standard economics, only extended tomultiple dimensions. For example, the following figure showssales for the whole market and for a firm for different levels ofthe represented firm’s qualities, assuming the product spacemade of 2 characteristics.


Overall market dynamics


However, static demand functions are theoretical concepts,while in reality we can observe choices of people through time.The model can then be best explored assuming a market for anovel product, and assessing how different conditions cangenerate different market structures.

We build a model assuming that consumers enter the marketaccording to a s-shaped dynamics. The dynamics isrepresented with a contagion diffusion dynamics where eachconsumer introduces a decreasing number of new consumers’to the market.


Overall market dynamics

1 75 150 225 300

1

490

979

1468

1957


Consumers’ learning

We assume that consumers’ learn through time, making largemistakes at the beginning and then being increasingly able toassess the true products’ qualities. This is represented bydecreasing the parameter ∆ determining the width of theprobability function.


Consumers’ learning

We assume that consumers’ learn through time, making largemistakes at the beginning and then being increasingly able toassess the true products’ qualities. This is represented bydecreasing the parameter ∆ determining the width of theprobability function.

In effect we turn the parameter into a variable ∆age for eachconsumer where we set the initial level ∆0 representing thenewbies’ error and the final limit ∆∞ as the error constantlymade by even expert consumers.


Single consumers’ learning

1 75 150 225 300

4e−06

5

10

15

20


Exercises

We can now observe and interpret the results produced bydifferent configurations of the model. We will show the numberof consumers adopting one among ten products. In the differentexercises we will modify the following aspects:

Products’ values and marketing strategies vxi ’s and kx

i ’s ;


Exercises



i ’s ;

Learning limits ∆∞


Exercises



i ’s ;


Tolerance levels τ


Exercises



i ’s ;


Tolerance levels τ

Relevance of peer’s pressure in preferences formation δ


Simple monopoly

As initial test let’s consider the supply side composed by allidentical products, except one which is superior to competitorsin all respects.


Simple monopoly

As initial test let’s consider the supply side composed by allidentical products, except one which is superior to competitorsin all respects.

We assume that consumers’ have no tolerance τ = 0 and can,with age, perfectly read the true products’ values ∆∞ = 0.


Monopoly

1 75 150 225 300

0

489.25

978.5

1467.75

1957


Monopoly with errors

Suppose that consumers maintain the possibility to make(small) errors in evaluating products even when the are expert,∆∞ > 0. In this case the dominating product keeps the marketleadership, but small shares of consumers keep on erroneouslychoosing dominated products.


Monopoly with errors

1 75 150 225 300

0

170.25

340.5

510.75

681


Monopoly with tolerance

In this last case on monopoly we introduce the “tolerance”. Inrespect of the previous exercises we assume that consumerconsider as inferior only products whose values is less than τ%that of the maximum. We set the value such that the dominantproduct enjoyes an advantage that, in effect, is not perceived asrelevant by consumers.



1 100 200 300 400

0

133.25

266.5

399.75

533



The reason lies in the probability distribution of the errors ofconsumers. When the consumers reach the stage where∆age = 0 they obviously realise that the advantage of thedominant firm is negligible. However, before that stage, thepossibility of errors actually favours the dominant firm, sinceconsumers have a large chance to mis-interpret the gap aslarger than the actual one.


Segmentation and concentration

Let’s consider now a set of suppliers as “specialized”producers. Each of the 10 competitor enjoys an advantage inrespect of one of 10 characteristics of the products, andpursue, accordingly, a marketing strategy promoting thatcharacteristic. Consumers have no tolerance (τ = 0) andperfectly learn to evaluate products (∆∞ = 0).We compare the effect of a higher and lower δ, governing theconcentration or diffusion of the probabilities when forming thepreferences.


Segmentation and concentration

1 75 150 225 300

0

57.25

114.5

171.75

229

1 75 150 225 300

0

80.75

161.5

242.25

323

Low δ High δ


“Perfect” oligopoly

Let’s now consider a large number of firms, initialized withrandom values of qualities and market strategies. We make afirst test assuming consumers with no tolerance and perfectlearning (τ = 0 and ∆∞ = 0).


“Perfect” oligopoly

1 75 150 225 300

0

56.25

112.5

168.75

225


“Noisy” oligopoly

In the same setting we now prevent consumers to reach perfectevaluation, setting ∆∞ > 0 until period 400, and then weabruptly set ∆∞ = 0.


“Noisy” oligopoly

1 150 300 450 600

0

56.25

112.5

168.75

225


“Chaotic” oligopoly

In this last exercise we set perfect learning, ∆∞ = 0, butintroduce a small tolerance, τ > 0, meaning that consumersconsider equivalent products on characteristics differing bysmall values.


“Chaotic” oligopoly

1 75 150 225 300

0

87.5

175

262.5

350


Demand matters

The two complex market configurations are similar in terms ofdistributional terms: concentration, stability, etc. However, theranking of firms is very different: firms succeeding in onemarket have only mediocre performance in the other.

This difference shows that demand matters, and evaluatingonly on the basis of supply-side features fails to catch crucialaspects. The following graph reports the sales of firms in thetwo markets.


Comparison


Conclusions

We presented a model for consumers providing a cleardistinction between decision making procedure, preferencesand actual choices produced.


Conclusions


The model is able to generate a wide variety of marketconfigurations allowing to define a classification of marketsegmentation.


Conclusions


The model is able to generate a wide variety of marketconfigurations allowing to define a classification of marketsegmentation.

Each configuration is rooted in motivations concerning featuresof the demand side that are potentially observable.


Conclusions

In particular, we identified the following types of marketsegmentation:

1 Error-based segmentation. Consumers willing to choosethe best in respect of one characteristic actually distributeacross a range of firms. However, all users of a givenproduct have the same objective.


Conclusions

In particular, we identified the following types of marketsegmentation:

1 Error-based segmentation. Consumers willing to choosethe best in respect of one characteristic actually distributeacross a range of firms. However, all users of a givenproduct have the same objective.

2 Complex segmentation. Consumers aim at a several,ordered, goals, generating complex market structures.Users of the same products have different reasons for theirchoices.


Conclusions

The research may be extended in several directions:

The basic TTB used can be extended to include apre-filtering of products removing those not affordable byconsumers, or however not fitting a set of minimalrequirements.


Conclusions



The model may be systematically studied assumingheterogeneous classes of consumers, and extended toinclude a dynamic supply side.


Conclusions



The model may be systematically studied assumingheterogeneous classes of consumers, and extended toinclude a dynamic supply side.

Relevant parameters of the model are observable, so thatthe model may be used for applied purposes.

boundedly rational consumers · two product in respect of one single characteristic, v∗x i and v...

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