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Investigating the impact of customer stochasticity on firm price discrimination strategies using a new Bayesian mixture scale heterogeneity model


In this paper, we study the impact of customer stochasticity on firm price discrimination strategies. We develop a new model termed the Bayesian Mixture Scale Heterogeneity (BMSH) model that incorporates both parameter heterogeneity and customer stochasticity using a mixture model approach, and demonstrate model identification using extensive simulations. We estimate the model on yogurt scanner data and find that compared to the benchmark mixed logit and multinomial probit models, our model shows that markets are less price elastic, and that a majority of customers exhibit stochasticity in purchases; our model also obtains better prediction and more profitable targeting strategies.

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  1. 1.

    The Web Appendix material is available from the authors on request.

  2. 2.

    While for simplicity, we maintain the same true value of the price coefficient for the MIXL and HetSMNL utility components of the BMSH model; we have conducted additional simulations to ensure that the true values are recovered when these coefficients are different (\( {\beta}_p^M\ne {\beta}_p^S \)). Results are available from the authors on request.

  3. 3.

    We term this as heterogeneous SMNL (HetSMNL) to distinguish it from the SMNL model of Fiebig et al. (2010) (Figure 1, page 398) which does not have heterogeneity in the ASCs.

  4. 4.

    However, in the case of 70 % MIXL, NP = 100, T=10, price coefficient = −6, the MNP model does not converge well and shows multimodality in the posterior distribution.

  5. 5.

    However, we note that the DIC measure may not always give accurate values for mixture models. We thank an anonymous reviewer for pointing this out (see Geweke and Keane 2006).

  6. 6.

    These figures for the other three brands as focal brands are available from the authors on request.

  7. 7.

    We have examined conditions under which targeted coupon face values are higher for two different discrete choice models and find that this is related to the differing price coefficients as well as the magnitude of difference between the odds computed using the two different models. The factors affecting different optimal coupon face values are thus more nuanced than just a comparison of price coefficients or price elasticities in the two models would suggest. Further results are available from the authors on request.


  1. Ben-Akiva, M., & Lerman, S. (1985). Discrete choice analysis: theory and application to travel demand. Cambridge: MIT Press.

    Google Scholar 

  2. Chintagunta, P. K. (1992). Heterogeneity in nested logit models: an estimation approach and empirical results. International Journal of Research in Marketing, 9(2), 161–175.

    Article  Google Scholar 

  3. Feit EM (2009) Extending the generalized multinomial logit model: error scale and decision-maker characteristics. Accessed August 23, 2012.

  4. Fiebig, D. G., Keane, M. P., Louviere, J., & Wasi, N. (2010). The generalized multinomial logit model: accounting for scale and coefficient heterogeneity. Marketing Science, 29(3), 393–421.

    Article  Google Scholar 

  5. Geweke, J., & Keane, M. (2006). Smoothly mixing regressions. Journal of Econometrics, 138(1), 252–290.

    Article  Google Scholar 

  6. Hartmann, W. R. (2010). Demand estimation with social interactions and the implications for targeted marketing. Marketing Science, 29(4), 585–601.

    Article  Google Scholar 

  7. Hutchinson, J. W., Zauberman, G., & Meyer, R. (2010). Commentary—on the interpretation of temporal inflation parameters in stochastic models of judgment and choice. Marketing Science, 29(1), 23–31.

    Article  Google Scholar 

  8. Jain, D. C., Vilcassim, N. J., & Chintagunta, P. K. (1994). A random-coefficients logit brand-choice model applied to panel data. Journal of Business & Economic Statistics, 12(3), 317–328.

    Google Scholar 

  9. Kasahara, H., & Shimotsu, K. (2009). Nonparametric identification of finite mixture models of dynamic discrete choices. Econometrica, 77(1), 135–175.

    Article  Google Scholar 

  10. Maddala, G. (1983). Limited-dependent and qualitative variables in econometrics. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  11. Pancras, J., & Sudhir, K. (2007). Optimal marketing strategies for a customer data intermediary. Journal of Marketing Research, 44(4), 560–578.

    Article  Google Scholar 

  12. Quandt, R. E. (1972). A new approach to estimating switching regressions. Journal of the American Statistical Association, 67(338), 306–310.

    Article  Google Scholar 

  13. Rossi, P. E., McCulloch, R. E., & Allenby, G. M. (1996). The value of purchase history data in target marketing. Marketing Science, 15(4), 321–340.

    Article  Google Scholar 

  14. Salisbury, L. C., & Feinberg, F. M. (2010a). Alleviating the constant stochastic variance assumption in decision research: theory, measurement, and experimental test. Marketing Science, 29(1), 1–17.

    Article  Google Scholar 

  15. Salisbury, L. C., & Feinberg, F. M. (2010b). Rejoinder-temporal stochastic inflation in choice-based research. Marketing Science, 29(1), 32–39.

    Article  Google Scholar 

  16. Singh, V. P., Hansen, K. T., & Gupta, S. (2005). Modeling preferences for common attributes in multicategory brand choice. Journal of Marketing Research, 42(2), 195–209.

    Article  Google Scholar 

  17. Tirole, J. (1988). The theory of industrial organization. Cambridge: MIT Press.

    Google Scholar 

  18. Titterington, D. M., Smith, A. F., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions (Vol. 7). New York: Wiley.

    Google Scholar 

  19. Zhang, J., & Wedel, M. (2009). The effectiveness of customized promotions in online and offline stores. Journal of Marketing Research, 46(2), 190–206.

    Article  Google Scholar 

  20. Zhang, J. Z., Netzer, O., & Ansari, A. (2014). Dynamic targeted pricing in B2B relationships. Marketing Science, 33(3), 317–337.

    Article  Google Scholar 

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Correspondence to Joseph Pancras.

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Pancras, J., Wang, X. & Dey, D.K. Investigating the impact of customer stochasticity on firm price discrimination strategies using a new Bayesian mixture scale heterogeneity model. Mark Lett 27, 537–552 (2016).

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  • Targeted marketing
  • Customer stochasticity
  • Scale heterogeneity
  • Mixture models
  • Price discrimination
  • Bayesian estimation