# Contagion of network products in small-world networks

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## Abstract

We formulate a model in which agents embedded in an exogenous social network decide whether to adopt a new network product or not. In the theoretical part of the paper, we characterize the stochastically stable equilibria for *complete networks* and *cycles*. For an arbitrary network structure, we develop a novel graph decomposition method to characterize the set of recurrent communication states, which is a superset of stochastically stable equilibria of the adoption game presented in our model. In the simulation part, we study the contagion process of a network product in small-world networks that systematically represent social networks. We simulate a generalization of the Morris (Rev Econ Stud 67(1):57–78, 2000) Contagion model that can explain the chasm between *early adopters* and *early majority*. Our numerical analysis shows that the failure of a new network product is less likely in a highly cliquish network. In addition, the contagion process reaches to steady state faster in random networks than in highly cliquish networks. It turns out that marketers should work with mixed marketing strategies, which will result in a full contagion of a network product and faster contagion rates with a higher probability.

## Keywords

Social network Contagion Simulation Cliquish network Random network Small-world network## JEL Classification

A14 C63 D12 D71 D91## Notes

### Acknowledgements

I thank the editor, the associate editor, and two anonymous reviewers for their thoughtful and constructive comments. I am also indebted to Semih Akçomak, Pelin Akyol, Rahmi İlkılıç, Ayşe Özgür Pehlivan, and Kemal Yıldız for helpful conversations and discussions. The views expressed here are my own and do not necessarily reflect those of the Presidency of the Republic of Turkey Presidency of Strategy and Budget. Any errors are my own.

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