Games in Management Science pp 15-39 | Cite as

# On the Modelling of Price Effects in the Diffusion of Optional Contingent Products

## Abstract

In this chapter, we study the pricing strategies of firms in a multi-product diffusion model where we use a new formalization of the price effects. More particularly, we introduce the impact of prices on one of the factors that affect the diffusion of new products: the innovation coefficient. By doing so, we relax one of the hypotheses in the existing literature stating that this rate is constant. In order to assess the impact of this functional form on the pricing policies of firms selling optional contingent products, we use our model to study two scenarios already investigated in the multiplicative form model suggested by Mahajan and Muller (M&M).

We follow a “logical experimentation” perspective by computing and comparing the results of three models: (1) The M&M model, (2) a modified version of M&M where the planning horizon is infinite, and (3) our model, where the new formalization of the innovation effect is introduced. This perspective allows us to attribute the differences in results to either the length of the planning horizon or to our model’s formalization. Besides its contribution to the literature on pricing and diffusion, this paper highlights the sensitivity of results to the hypothesis used in product diffusion modelling and could explain the mixed results obtained in the empirical validations of diffusion models.

## Keywords

Marketing modelling Diffusion models Dynamic pricing Contingent products## Notes

### Acknowledgements

We are grateful to two anonymous reviewers for valuable comments and suggestions on an earlier draft of this paper. This research is partially supported by Spanish MINECO under projects ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León under projects VA105G18 and VA024P17 co-financed by FEDER funds (EU).

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