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Modeling Competitive Responsiveness and Game Theoretic Models

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Advanced Methods for Modeling Markets

Part of the book series: International Series in Quantitative Marketing ((ISQM))

Abstract

The study of competition and competitive responsiveness has a long tradition, involving a variety of models developed and applied in many different situations. In this chapter we give a brief survey of specific applications and methodologies used to model competitive responsiveness. In addition, we attend to the use of competitive response models for normative decision-making and introduce game theoretic models.

A part of this chapter is based on Leeflang (2008a, 2008b).

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Notes

  1. 1.

    Aboulnasr et al. (2008); Moe and Yang (2009).

  2. 2.

    Cleeren et al. (2006); Cleeren et al. (2010).

  3. 3.

    Ailawadi et al. (2010); Gielens et al. (2008); Singh et al. (2006).

  4. 4.

    Sriram and Kadiyali (2009).

  5. 5.

    To make sure this expression for \({a}_{\mathit{opt}}\) corresponds to a maximum, second-order conditions are examined. We find that, given the assumptions about \( {\widehat{\beta}}_a \), \( {\widehat{\beta}}_{a_c\ } \), and p-c, the second-order condition is expected to be negative which leads to a maximum value of π.

  6. 6.

    For a more in-dept. review, see for example Alsem and Leeflang (1994) and Alsem et al. (1989).

  7. 7.

    Urban and Karash (1971).

  8. 8.

    The numbers refer to the sets of models that we distinguish in Fig. 9.1.

  9. 9.

    Examples are Friedman (1958); Krishnan and Gupta (1967).

  10. 10.

    See Kadiyali et al. (2001) for a review.

  11. 11.

    Examples are models developed by Ellison (1994) and Sudhir et al. (2005).

  12. 12.

    The model of Ailawadi et al. (2005) has these features: see Sect. 9.5.3.

  13. 13.

    See, for example, Alsem et al. (1989).

  14. 14.

    In (9.13) and (9.14) \( \frac{\partial {Q}_T}{\partial a},\frac{\partial {m}_j}{\partial a} \) are the direct effects and \( \frac{\partial Q}{\partial a},\frac{\partial m}{\partial a} \) are the total effects.

  15. 15.

    The time is omitted for convenience. Some of the variables in the reaction functions were specified with a one-period lag.

  16. 16.

    In (9.21) the “subtraction” of x ℓjt means that instrument ℓ for brand j in period t is not a predictor variable.

  17. 17.

    For example, suppose that n = 7 (brands) each with five instruments, T* = 10(lagged periods), and T = 76. Then we have 76 observations to estimate 391 parameters, under the assumption that all manufacturers use all marketing instruments.

  18. 18.

    For a discussion of other models that calibrate competitive reaction functions, see Kadiyali et al. (1999) and Vilcassim et al. (1999). In all cases, the reaction functions attempt to capture the use of marketing instruments to react to changes in other instruments without regard to consumer responses.

  19. 19.

    See for a discussion about modeling asymmetric competition: Foekens et al. (1997); Leeflang et al. (2000, Sect. 14.4) and Vol. I, Sect. 7.3.3.3.

  20. 20.

    This text is based on Van Heerde et al. (2015).

  21. 21.

    We closely follow Horváth et al. (2005). For a thorough discussion of VARX-models see also Dekimpe et al. (2008) and Chap. 4. Other examples of VARX-models that are used to model competitive response are Srinivasan et al. (2000); Takada and Bass (1998).

  22. 22.

    They do not include separate lagged non-price instruments to reduce concerns about the degrees of freedom.

  23. 23.

    More complete treatments of game theory in a marketing context can be found in Hanssens et al. (2001, pp. 367–374); Moorthy (1985). A managerial treatment of game theoretic principles appears in Nalebuff et al. (1996). For a general introduction to modern game theory, see Fudenberg and Tirole (1991); Mass-Calell et al. (1995).

  24. 24.

    We closely follow Kadiyali et al. (2001).

  25. 25.

    See also Chap. 5 on Structural Models.

  26. 26.

    See, for example, Chintagunta and Rao (1996); Sudhir (2001); Sudhir et al. (2005); Zhu et al. (2009).

  27. 27.

    We closely follow Roy et al. (2006).

  28. 28.

    We closely follow Draganska et al. (2010).

  29. 29.

    The system of equations should have a negative- definite Hessian matrix. See for a similar model Villas-Boas and Zhao (2005).

  30. 30.

    See Sudhir et al. (2005).

  31. 31.

    Ataman et al. (2007); Ataman et al. (2008); Van Heerde et al. (2004) and Chap. 5.

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Authors and Affiliations

  1. Department of Marketing, Faculty of Economics and Business, University of Groningen, Groningen, The Netherlands

    Peter S. H. Leeflang

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  1. Peter S. H. Leeflang
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Correspondence to Peter S. H. Leeflang .

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Editors and Affiliations

  1. Department of Marketing, University of Groningen, Groningen, The Netherlands

    Peter S. H. Leeflang

  2. Department of Marketing, University of Groningen, Groningen, The Netherlands

    Jaap E. Wieringa

  3. Department of Marketing, University of Groningen, Groningen, The Netherlands

    Tammo H.A Bijmolt

  4. Department of Marketing, D’Amore-McKim School of Business, Northeastern University, Boston, USA

    Koen H. Pauwels

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Leeflang, P.S.H. (2017). Modeling Competitive Responsiveness and Game Theoretic Models. In: Leeflang, P., Wieringa, J., Bijmolt, T., Pauwels, K. (eds) Advanced Methods for Modeling Markets. International Series in Quantitative Marketing. Springer, Cham. https://doi.org/10.1007/978-3-319-53469-5_9

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