# The Diffusion of Competitive Platform-Based Products with Network Effects

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Research on Network Effects

#### 2.2. Research on Two-Sided Platforms

#### 2.3. Research on Product Diffusion

## 3. The Model

#### 3.1. Consumer Decisions

#### 3.2. Seller Decisions

- (1)
- The sellers who has not joined any platform and who will continue to do so will gain no profit; if the sellers choose to join platform $k$, they will gain net profits ${\pi}_{jkt}({n}_{kt}^{E},{M}_{kt}^{E})-l{c}_{j}$, where $l{c}_{j}$ is the learning cost incurred from preparing to produce a compatible product or service, which is assumed to be a normally distributed random variable, $N(E(l{c}_{j}),Var(l{c}_{j}))$.
- (2)
- A seller on platform $k$ will gain ${\pi}_{jkt}({n}_{kt}^{E},{M}_{kt}^{E})$ when continuing to stay on; if sellers withdraws from platform k and will not join any platform, they will gain no profit; if they join the other platform, then the net profits are ${\pi}_{j{k}^{\prime}t}({n}_{{k}^{\prime}t}^{E},{M}_{{k}^{\prime}t}^{E})-l{c}_{j}$.

#### 3.3. Complex User Network Construction

- (1)
- Start with order: Construct a ring-shaped network consisting of $N$ nodes, where each node $i$ is adjacent to its neighboring nodes, $i=1,2,\mathrm{\dots},K/2$, with $K$ being even. Here, the nodes represent users.
- (2)
- Randomization: Add shortcuts between randomly chosen pairs of nodes with probability $p$.

## 4. Computing Settings

## 5. Results Analysis

#### 5.1. Properties of Platform Diffusion with Direct and Indirect Network Effects

#### 5.2. First-Mover Advantage—The Number of Users and Available Complementary Products

#### 5.3. Iteration of Platforms and Consumer Heterogeneity

#### 5.4. Effects of Switching and Learning Costs on Platform Competition

## 6. Conclusions and Discussion

#### 6.1. Theoretical Implications

#### 6.2. Practical Implications

#### 6.3. Limitations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Mantena, R.; Sankaranarayanan, R.; Viswanathan, S. Platform-based information goods: The economics of exclusivity. Decis. Support Syst.
**2010**, 50, 79–92. [Google Scholar] [CrossRef] - Andersen, R.; Brunoe, T.D.; Nielsen, K. Platform-based product development in the process industry: A systematic literature review. Int. J. Prod. Res.
**2022**, 61, 1696–1719. [Google Scholar] [CrossRef] - Rochet, J.C.; Tirole, J. Platform competition in two-sided markets. J. Eur. Econ. Assoc.
**2003**, 1, 990–1029. [Google Scholar] [CrossRef] - Armstrong, M. Competition in two-sided markets. RAND J. Econ.
**2006**, 37, 668–691. [Google Scholar] [CrossRef] - Carrillo, J.D.; Tan, G. Platform competition with complementary products. Int. J. Ind. Organ.
**2021**, 77, 102741. [Google Scholar] [CrossRef] - Katz, M.L.; Shapiro, C. Network externalities, competition, and compatibility. Am. Econ. Rev.
**1985**, 75, 424–440. [Google Scholar] - Goldenberg, J.; Libai, B.; Muller, E. Riding the Saddle: How Cross-Market Communications Can Create a Major Slump in Sales. J. Mark.
**2002**, 66, 1–16. [Google Scholar] [CrossRef] - Lieven, S.D.M.; Gino, B.V. ICT-innovations today: Making traditional diffusion patterns obsolete, and preliminary insight of increased importance. Telemat. Inform.
**2004**, 21, 235–260. [Google Scholar] [CrossRef] - Peres, R.; Muller, E.; Mahajan, V. Innovation diffusion and new product growth models: A critical review and research directions. Int. J. Res. Mark.
**2010**, 27, 91–106. [Google Scholar] [CrossRef] - Barabási, A.-L.; Albert, R. Emergence of Scaling in Random Networks. Science
**1999**, 286, 509–512. [Google Scholar] [CrossRef] - Yang, M.; Abubakar, A.H.; Jiang, P. Deep learning and complex network theory based analysis on socialized manufacturing resources utilisations and an application case study. Concurr. Eng.
**2021**, 29, 236–248. [Google Scholar] [CrossRef] - Watts, D.J.; Strogatz, S.H. Collective dynamics of ‘small-world’ networks. Nature
**1998**, 393, 440–442. [Google Scholar] [CrossRef] [PubMed] - Shang, Y. Sombor index and degree-related properties of simplicial networks. Appl. Math. Comput.
**2021**, 419, 126881. [Google Scholar] [CrossRef] - Thompson, P. Learning by doing. Handb. Econ. Innov.
**2010**, 1, 429–476. [Google Scholar] - Li, Y.; Ping, Y.; Zhong, Y.; Misra, R. Learning-by-doing in non-homogeneous tasks: An empirical study of content creator performance on a music streaming platform. Electron. Commer. Res. Appl.
**2023**, 58, 101241. [Google Scholar] [CrossRef] - Chou, C.F.; Shy, O. Network effects without network externalities. Int. J. Ind. Organ.
**1990**, 8, 259–270. [Google Scholar] [CrossRef] - Katz, M.L.; Shapiro, C. Systems Competition and Network Effects. J. Econ. Perspect.
**1994**, 8, 93–115. [Google Scholar] [CrossRef] - Abrahamson, E.; Rosenkopf, L. Social Network Effects on the Extent of Innovation Diffusion: A Computer Simulation. Organ. Sci.
**1997**, 8, 289–309. [Google Scholar] [CrossRef] - Bertrand, M.; Luttmer, E.F.P.; Mullainathan, S. Network Effects and Welfare Cultures. Q. J. Econ.
**2000**, 115, 1019–1055. [Google Scholar] [CrossRef] - Farrell, J.; Klemperer, P. Coordination and lock-in: Competition with switching costs and network effects. In Handbook of Industrial Organization; Elsevier: Amsterdam, The Netherlands, 2007; Volume 3, pp. 1967–2072. [Google Scholar]
- Fainmesser, I.P.; Galeotti, A. Pricing network effects. Rev. Econ. Stud.
**2015**, 83, 165–198. [Google Scholar] [CrossRef] - Belleflamme, P.; Peitz, M. Platforms and network effects. In Handbook of Game Theory and Industrial Organization; Edward Elgar Publishing: Cheltenham, UK, 2018; Volume II, pp. 286–317. [Google Scholar]
- Sui, R.; Zhang, X.; Dan, B.; Zhang, H.; Liu, Y. Bilateral value-added service investment in platform competition with cross-side network effects under multihoming. Eur. J. Oper. Res.
**2023**, 304, 952–963. [Google Scholar] [CrossRef] - Kim, J.; Lee, D.-J.; Ahn, J. A dynamic competition analysis on the Korean mobile phone market using competitive diffusion model. Comput. Ind. Eng.
**2006**, 51, 174–182. [Google Scholar] [CrossRef] - Tsai, B.-H.; Li, Y.; Lee, G.-H. Forecasting global adoption of crystal display televisions with modified product diffusion model. Comput. Ind. Eng.
**2010**, 58, 553–562. [Google Scholar] [CrossRef] - Kimura, M. Effects for console game sales in Japan market. Asia Pac. J. Mark. Logist.
**2015**, 27, 61–81. [Google Scholar] [CrossRef] - Parker, G.G.; Van Alstyne, M.W. Two-Sided Network Effects: A Theory of Information Product Design. Manag. Sci.
**2005**, 51, 1494–1504. [Google Scholar] [CrossRef] - Eisenmann, T.; Parker, G.; Van Alstyne, M.W. Strategies for two-sided markets. Harv. Bus. Rev.
**2006**, 84, 92. [Google Scholar] - Weyl, E.G. A Price Theory of Multi-Sided Platforms. Am. Econ. Rev.
**2010**, 100, 1642–1672. [Google Scholar] [CrossRef] - Zhu, F.; Iansiti, M. Entry into platform-based markets. Strat. Manag. J.
**2011**, 33, 88–106. [Google Scholar] [CrossRef] - Dou, G.; Lin, X.; Xu, X. Value-added service investment strategy of a two-sided platform with the negative intra-group network externality. Kybernetes
**2018**, 47, 937–956. [Google Scholar] [CrossRef] - Rysman, M. The Economics of Two-Sided Markets. J. Econ. Perspect.
**2009**, 23, 125–143. [Google Scholar] [CrossRef] - Wei, X.; Gong, H.; Song, L. Product diffusion in dynamic online social networks: A multi-agent simulation based on gravity theory. Expert Syst. Appl.
**2023**, 213, 119008. [Google Scholar] [CrossRef] - Rohlfs, J.H. Bandwagon Effects in High-Technology Industries; MIT Press: Cambridge, MA, USA, 2003. [Google Scholar]
- Tellis, G.; Yin, E.; Niraj, R. Does Quality Win? Network Effects versus Quality in High-Tech Markets. J. Mark. Res.
**2009**, 46, 135–149. [Google Scholar] [CrossRef] - Himmelberg, C.; Economides, N. Critical mass and network evolution in telecommunications. In Toward a Competitive Telecommunication Industry; Routledge: New York, NY, USA, 2013; pp. 59–76. [Google Scholar]
- Goldenberg, J.; Libai, B.; Muller, E. The chilling effects of network externalities. Int. J. Res. Mark.
**2010**, 27, 4–15. [Google Scholar] [CrossRef] - Iyengar, R.; Van den Bulte, C.; Valente, T.W. Rejoinder—Further reflections on studying social influence in new product diffusion. Mark. Sci.
**2011**, 30, 230–232. [Google Scholar] [CrossRef] - Gupta, S.; Jain, D.C.; Sawhney, M.S. Modeling the Evolution of Markets with Indirect Network Externalities: An Application to Digital Television. Mark. Sci.
**1999**, 18, 396–416. [Google Scholar] [CrossRef] - Weitzel, T.; Beimborn, D.; König, W. A Unified Economic Model of Standard Diffusion: The Impact of Standardization Cost, Network Effects, and Network Topology. MIS Q.
**2006**, 30, 489. [Google Scholar] [CrossRef] - Stremersch, S.; Tellis, G.J.; Franses, P.H.; Binken, J.L. Indirect network effects in new product growth. J. Mark.
**2007**, 71, 52–74. [Google Scholar] [CrossRef] - Chun, S.Y.; Hahn, M. A diffusion model for products with indirect network externalities. J. Forecast.
**2008**, 27, 357–370. [Google Scholar] [CrossRef] - Gong, X.; Liu, Z.; Zheng, X.; Wu, T. Why are experienced users of WeChat likely to continue using the app? Asia Pac. J. Mark. Logist.
**2018**, 30, 1013–1039. [Google Scholar] [CrossRef] - Yu, Z.; Li, S.; Tong, L. Market dynamics and indirect network effects in electric vehicle diffusion. Transp. Res. Part D Transp. Environ.
**2016**, 47, 336–356. [Google Scholar] [CrossRef] - DelRe, S.A.; Jager, W.; Janssen, M.A. Diffusion dynamics in small-world networks with heterogeneous consumers. Comput. Math. Organ. Theory
**2006**, 13, 185–202. [Google Scholar] [CrossRef] - Choi, H.; Kim, S.-H.; Lee, J. Role of network structure and network effects in diffusion of innovations. Ind. Mark. Manag.
**2010**, 39, 170–177. [Google Scholar] [CrossRef] - Katona, Z.; Zubcsek, P.P.; Sarvary, M. Network Effects and Personal Influences: The Diffusion of an Online Social Network. J. Mark. Res.
**2011**, 48, 425–443. [Google Scholar] [CrossRef] - Spulber, D. Firms and Networks in Two-Sided Markets. In The Handbook of Economics and Information Systems; Elsevier: Amsterdam, The Netherlands, 2006. [Google Scholar]
- Newman, M.; Watts, D. Renormalization group analysis of the small-world network model. Phys. Lett. A
**1999**, 263, 341–346. [Google Scholar] [CrossRef] - Li, Q.; Yao, H.; Mai, T.; Jiang, C.; Zhang, Y. Reinforcement-Learning- and Belief-Learning-Based Double Auction Mechanism for Edge Computing Resource Allocation. IEEE Internet Things J.
**2019**, 7, 5976–5985. [Google Scholar] [CrossRef] - Kretschmer, T.; Leiponen, A.; Schilling, M.; Vasudeva, G. Platform ecosystems as meta-organizations: Implications for platform strategies. Strateg. Manag. J.
**2021**, 43, 405–424. [Google Scholar] [CrossRef] - Farronato, C.; Fong, J.; Fradkin, A. Dog Eat Dog: Balancing Network Effects and Differentiation in a Digital Platform Merger. Manag. Sci.
**2023**. [Google Scholar] [CrossRef] - McIntyre, D.P.; Subramaniam, M. Strategy in Network Industries: A Review and Research Agenda. J. Manag.
**2009**, 35, 1494–1517. [Google Scholar] [CrossRef] - Li, H.; Zhao, N. Better earlier than longer: First-Mover Advantage in social commerce product information competition. Sustainability
**2019**, 11, 4630. [Google Scholar] [CrossRef]

**Figure 1.**Competitive platform diffusion on the user and seller sides with the same initial conditions.

Parameter | Value | ||
---|---|---|---|

A | B | ||

N | Size of consumer population | 200 | |

M | Size of seller population | 20 | |

N_{k0} | Initial install bases of users | 20 | 20 |

M_{k0} | Initial install bases of users | 2 | 2 |

α_{1k} | Strength of direct network effect | 2 | 2 |

α_{2k} | Strength of indirect network effect | 2 | 2 |

β_{1} | Index of direct networks | 1.5 | |

β_{2} | Index of indirect network effect | 2 | |

σ | Index of CES utility | 0.5 | |

υ_{0k} | Intrinsic value of platforms | 5 | 5 |

K | Average number of neighbors of user | 8 | |

λ | Switching costs | 0.5 | 0.5 |

p_{kt} | Price of platforms | 15 | 15 |

γ_{b} | Adaptive expectation coefficient of users | 0.5 | |

γ_{s} | Adaptive expectation coefficient of sellers | 0.5 | |

E(I_{it}) | Users’ budget expectations | 10 | |

Var(I_{it}) | Users’ budget variance | 4 | |

c | Marginal cost of sellers | 10 | |

E(lc_{jt}) | Sellers’ expected learning costs | 100 | |

Var(Ic_{jt}) | Variance in learning costs | 16 | |

ρ_{uk} | Expectation factors of users | 1 | 1 |

ρ_{sk} | Expectation factors of sellers | 0.1 | 0.1 |

ρ | Probability of randomly added shortcuts | 0.2 |

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**MDPI and ACS Style**

Zhang, J.; Dong, L.; Ji, T.
The Diffusion of Competitive Platform-Based Products with Network Effects. *Sustainability* **2023**, *15*, 8845.
https://doi.org/10.3390/su15118845

**AMA Style**

Zhang J, Dong L, Ji T.
The Diffusion of Competitive Platform-Based Products with Network Effects. *Sustainability*. 2023; 15(11):8845.
https://doi.org/10.3390/su15118845

**Chicago/Turabian Style**

Zhang, Jie, Lingfeng Dong, and Ting Ji.
2023. "The Diffusion of Competitive Platform-Based Products with Network Effects" *Sustainability* 15, no. 11: 8845.
https://doi.org/10.3390/su15118845