Online-Offline Competition with Heterogeneous Consumers: An Example for No Existence of Pure Strategy Nash Equilibrium

Authors

  • Weixing Ford Texas A&M University
  • Haipeng Han Tsinghua University
  • Jie Zheng Tsinghua University

DOI:

https://doi.org/10.21638/11701/spbu31.2022.04

Abstract

Existing literature on competition between online and offline firms has focused on market conditions that guarantee the existence of a pure strategy Nash equilibrium. In this note, by constructing a concrete example, we provide a first attempt to show that the equilibrium existence result does not necessarily hold when consumers' preferences are heterogeneous. Specifically, we consider the competition between one online firm and several offline firms in a market organized as a Salop model, where consumers' preferences have a binary distribution. We identify a boundary scenario where the type distribution is binary with one type of consumer loyal to online shopping and the other type loyal to offline shopping. We show that there is no pure strategy Nash equilibrium for this boundary scenario, which indicates that the market may not be stable under such conditions. Our study contributes to a better understanding of the equilibrium existence conditions for the online versus offline retail competition.

Keywords:

online versus offline, price competition, salop model, heterogeneous consumers, existence of equilibrium

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References

Balasubramanian, S. (1998). Mail versus mall: A strategic analysis of competition between direct marketers and conventional retailers. Marketing Science, 17(3), 181–195

Boyer, M. and Moreaux, M. (1993). Strategic market coverage in spatial competition. International Journal of Industrial Organization, 11(3), 299–326

Chen, Y., Hu, X. and Li, S. (2017). Quality differentiation and firms' choices between online and physical markets. International Journal of Industrial Organization, 52, 96–132

Fleckinger, P. and Lafay, T. (2010). Product flexibility and price competition in Hotelling's duopoly. Mathematical Social Sciences, 60(1), 61–68

Ford, W., Li, M., Li, Y. and Zheng, J. (2019). Competing channels for entering a local market. Working paper

Ford, W., Li, Y. and Zheng, J. (2021). Numbers of bricks and clicks: Price competition between online and offline stores. International Review of Economics & Finance, 75, 420–440

Forman, C., Ghose, A. and Goldfarb, A. (2009). Competition between local and electronic markets: How the benefit of buying online depends on where you live. Management science, 55(1), 47–57

Guo, W. C. and Lai, F. C. (2017). Prices, locations and welfare when an online retailer competes with heterogeneous brick-and-mortar retailers. The Journal of Industrial Economics, 65(2), 439–468

Han, H., Lian, Z. and Zheng, J. (2022). Online versus Offline Competition with Quadratic Transport Cost. Working paper

Han, H., Lien, D., Lien, J. W. and Zheng, J. (2022). Online or Face-to-Face? Competition among MOOC and Regular Education Providers. International Review of Economics & Finance, 80, 857–881

Hernandez, M. A. (2011). Nonlinear pricing and competition intensity in a hotelling-type model with discrete product and consumer types. Economics Letters, 110(3), 174–177

Hotelling, H. (1990). Stability in competition. In The collected economics articles of harold hotelling (pp. 50-–63). New York, NY: Springer

Kats, A. (1995). More on Hotelling's stability in competition. International Journal of Industrial Organization, 13(1), 89–93

Liu, Y., Gupta, S. and Zhang, Z. J. (2006). Note on self-restraint as an online entry-deterrence strategy. Management Science, 52(11), 1799–1809

Loginova, O. (2009). Real and virtual competition. The Journal of Industrial Economics, 57(2), 319–342

Madden, P. and Pezzino, M. (2011). Oligopoly on a Salop circle with centre. The BE Journal of Economic Analysis & Policy, 1(1)

Salop, S. C. (1979). Monopolistic competition with outside goods. The Bell Journal of Economics, 141–156

Wang, Q. and Zheng, J. (2020). Online versus offline: product differentiation and strategic consideration of choosing channels in market competition: Working paper

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Published

2023-01-25

How to Cite

Ford, W., Han, H., & Zheng, J. (2023). Online-Offline Competition with Heterogeneous Consumers: An Example for No Existence of Pure Strategy Nash Equilibrium. Contributions to Game Theory and Management, 15, 41–50. https://doi.org/10.21638/11701/spbu31.2022.04

Issue

Vol. 15 (2022)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.