Evolutionary demand: a model for boundedly rational consumers

Abstract

The paper is based on the acknowledgement that properties of markets stemming from features of demand are too frequently overlooked in the economic literature, particularly among evolutionary scholars. The overall goal is to show that “demand matters” to understand properly observed properties of markets not only because of its exogenous (i.e. non-economic) features, but also because of aspects of consumers’ behavior that fully deserve to be considered in the domain of economics. The paper presents a general model of the consumer based on a bounded rational decision algorithm. The model is shown to be compatible with available evidence on consumers’ behavior and adaptable for theoretical as well as empirical applications. The description of the proposed model’s components provides the opportunity to discuss a number of issues the importance of which for the analysis of markets of markets becomes evident taking a demand-oriented perspective. Among these, we propose a formal definition of preferences meant as decision criteria used by consumers and distinct from the actual decisions made by consumers at each purchasing occasion. We also highlight the potential role of firms’ marketing in shaping consumers’ preferences, suggesting an endogenous channel of influence on consumers’ preferences which is possibly highly relevant in certain markets. We use the model to show that the proposed model can easily replicate a generic market demand function, with the advantage of more robust foundations and greater flexibility in respect of standard consumer theory. We also show that limiting to consider distributional properties of markets, neglecting the type of demand, may lead to serious errors of interpretation.

Appendices

Appendix A: Simulation data setting

Table 3 reports the parameters values and variables initializations used in the simulations runs for the market segmentation experiments discussed in the paper. The table also briefly describes the main dynamics of the model not described in the main body of the paper. The code used for the generation of the results presented in the paper is available upon request.

Table 3 Initialization values for simulation runs

Appendix B: Robustness

The concept of robustness concerns the persistence of a claimed result varying the initialization of the model. How to support the claim of robustness of a result depends, obviously, on the nature of the result itself. For example, a simulation model may be used to assess properties of the whole time pattern of (some) variables, or only their final values. It may well be possible that simulation runs generated with different parameter values produce widely different patterns, all leading to essentially identical final values. Without a clear specification of the claimed results, one may contradictorily conclude that the results are at the same time robust and not robust. Hence the need to specify in detail the nature of the result and how it may be confirmed or rejected.

In our case, the claim is that two initializations of the model lead to final distribution of sales across firms with similar aggregate distributional properties, but generated by different ranking of firms by sales. We consider this core point as proven by the evidence presented in the main body of the paper. What we still need to show is the claim that the difference between the two cases depends on the two specific parameters differing in the two settings and not, instead, on other differences between the two models.

To reduce to the minimum the possible sources of differentiation between the two settings, the simulation experiments are purposefully built using exactly the same values for almost all parameters in the model. The only difference between the two experiments, besides the behavioral parameters discussed in the text, are the random values used during the simulation run (the random values drawn before starting the simulations, used to initialize product qualities and marketing strategies, are the same in both settings). Therefore, we need to perform a test directed to measure the robustness of our result in respect of the random events occurring during simulation runs.²⁴ We consider each of the two settings independently, aiming to show that each of them systematically provides identical results, and therefore it is legitimate to use a single representative run.

The model generates results depending partly on the deterministic structure of the model (initialization and deterministic equations) and partly on random factors. Random events are used in the following functions:

• Time of entry of new consumers.

• Characteristics’ values perceptions

• Preferences’ formation.

A few sample runs, using the same settings and different random series, show that the structural contributions are dominant in respect of random elements: in each of the test runs performed, every firm obtained almost identical results (i.e. market shares) with only fractional differences between different runs. For the sake of completeness, in this section we provide statistical evidence for the irrelevance of these random variations.

We compute a test for the hypothesis that the final level of sales for each firm is identical across different simulation runs. In other terms, the result would fail the test if we found that, across different repetitions of simulations with the same settings and different random events, firm sales assume very different values. In the following, we formalize the test reporting some statistical indicators computed on the data from different simulation runs.

We consider 10 runs generated with the same initial setting and using different series of random values. We assume that a model outcome (final firms’ sales levels) depends partly on their structural properties (initial values and dynamic equations) and partly on randomness. We consider each firm’s series as an instance of a (partly) stochastic process, the overall variance of which (structural and stochastic) can be approximated by the variance shown by the whole population of firms in a single run. Indicating with $x^{k}_{i}$ the final level of sales of firm i produced during the k ^th simulation run, and x ^k the average of all firms sales produced during simulation run k, we can then define the total variance of our series for simulation k as:

$$ \sigma^{T}_{k}= \frac{\sum^{N}_{i=1} \left(x^{k}_{i}- x^{k}\right)^{2}}{N}$$

Since we have 10 simulation runs, we can take the average of this variance over different runs to get a more reliable estimate of the total variance of the process generating the firms’ results.

$$ \sigma^{T} = \frac{\sum^{10}_{k=1} \sigma^{T}_{k}}{10} $$

We can consider this index the intra-simulation variance of our results; it is an estimation of the total variety that firms are subject to during a simulation run as the cumulative effect of structural and random effects.

To estimate the contribution of randomness, we use the values from each specific firm across different simulation runs. The variance computed over these 10 values (data for one firm over all simulation runs) will indicate the variety due to differing random events only, since the structural properties of the firm are the same across all simulations.

$$ \sigma^{R}_{i}= \frac{\sum^{10}_{k=1} \left(x^{k}_{i}- x_{i}\right)^{2}}{10}$$

where x _i is the average value for firm i across all the 10 simulation runs. Having 100 firms, we can take the average of 100 cross-simulation variances as an estimation of the variety induced by randomness only.

$$ \sigma^{R} = \frac{\sum^{N}_{i=1} \sigma^{R}_{i}}{N} $$

We call this index inter-simulation variance, because it indicates the variety generated by comparing structurally identical processes across simulations using different random events.

Table 4 reports the values for these indicators for the two simulation settings discussed in the paper. As a rough indicator of the distribution, we also report the maximum and minimum variance values obtained by the two samples of 10 simulations and 100 firms for the intra- and inter-simulation variance respectively. As an indication of the contribution of randomness to the model results, we report the ratio between inter-simulation variance and intra-simulation variance. This ratio will be 0 in case there were no variance due to randomness, that is, each firm provides perfectly identical results for each run. Conversely, the index would be 1 in case the variance across firms registered during a simulation run is identical to the variance registered by any given firm in different simulation runs.

Table 4 Robustness tests: intra- and inter-simulation variances

The data clearly indicate that the variance generated in any given run across all firms account for more than 99 % of the variance computed also across different runs. This can only be obtained if the values of sales for a firm differ from the values for other firms but is practically constant in different simulation runs.