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On the insufficiency of some conditions for minimal product differentiation

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Abstract

The basic framework is Hotelling’s model of product choice with quadratic transportation cost. Duopolists choose locations in the initial period and compete in prices in subsequent infinite periods. The firms share profits on the profit possibility frontier. Friedman and Thisse (Rand J Econ 24:631–645, 1993) provides a set of sufficient conditions for a unique equilibrium and minimal product differentiation in this setting. This paper reexamines those conditions. In the presence of some mild continuity requirements, there is exactly one profit sharing rule which satisfies those conditions. Furthermore, given any discount factor(s), the corresponding profits cannot be the outcome of a subgame perfect Nash equilibrium at every pair of locations. This brings out an inconsistency in the conditions. A slight weakening of the conditions, to allow for a wider class of profit sharing rules, can result in multiple equilibria and minimal product differentiation need not obtain. Two examples demonstrate this. Thus, neither those conditions nor their weaker variants can be used to characterize a unique equilibrium.

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References

  • Crawford, G.: Endogenous product choice: a progress report. Int J Ind Organ 30, 315–320 (2012)

    Article  Google Scholar 

  • Dasgupta, P., Maskin, E.: The existence of equilibrium in discontinuous economic games, I: theory. Rev Econ Stud 53, 1–26 (1986a)

    Article  Google Scholar 

  • Dasgupta, P., Maskin, E.: The existence of equilibrium in discontinuous economic games, II: applications. Rev Econ Stud 53, 27–41 (1986b)

    Article  Google Scholar 

  • d’Aspremont, C., Gabszewicz, J.J., Thisse, J.-F.: On Hotelling’s stability in competition. Econometrica 47, 1145–1150 (1979)

    Article  Google Scholar 

  • Friedman, J.W., Thisse, J.-F.: Partial collusion fosters minimum product differentiation. Rand J Econ 24, 631–645 (1993)

    Article  Google Scholar 

  • Hotelling, H.: Stability in competition. Econ J 39, 41–57 (1929)

    Article  Google Scholar 

  • Jehiel, P.: Product differentiation and price collusion. Int J Ind Organ 10, 633–641 (1992)

    Article  Google Scholar 

  • Matsumura, T., Matsushima, N.: Collusion, agglomeration, and heterogeneity of firms. Games Econ Behav 72, 306–313 (2011)

    Article  Google Scholar 

  • Rath, K.P.: Stationary and nonstationary strategies in Hotelling’s model of spatial competition with repeated pricing decisions. Int J Game Theory 27, 525–537 (1998)

    Article  Google Scholar 

  • Rath, K.P., Zhao, G.: Nonminimal product differentiation as a bargaining outcome. Games Econ Behav 42, 267–280 (2003)

    Article  Google Scholar 

  • Rath KP, Zhao G (2020) The nature of equilibria under noncollusive product design and collusive pricing. Mimeo (2020)

  • Reny, P.J.: Introduction to the symposium on discontinuous games. Econ Theory 61, 423–429 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

We are thankful to Thomas A. Gresik and Jeffrey M. Thurk for very helpful comments and suggestions. We are also indebted to an anonymous referee whose thoughtful comments led to many improvements in the paper.

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Correspondence to Kali P. Rath.

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Rath, K.P., Zhao, G. On the insufficiency of some conditions for minimal product differentiation. Econ Theory Bull 9, 53–65 (2021). https://doi.org/10.1007/s40505-020-00193-6

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  • DOI: https://doi.org/10.1007/s40505-020-00193-6

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