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Tractable Aggregation in Endogenous Network Formation Models

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  • Jose M. Betancourt

Abstract

This paper studies the long-run properties of a stochastic best-response network formation model. Players stochastically meet and make decisions about changing the state of their relationship. I give sufficient conditions under which this game induces a reversible Markov process in the space of networks, and show that in this case the stationary distribution is given by a Gibbs measure with an associated aggregating function that depends on players' utilities. Reversibility also implies the existence of a potential for a deterministic version of the network formation game. Using the properties of the Gibbs measure I show that, in simple settings, the long-run behavior of the model for increasingly large networks is driven by a trade-off between player incentives and the exponentially increasing number of feasible networks. I use this framework to obtain network statistics for simple models of social media following and international trade.

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  • Jose M. Betancourt, 2023. "Tractable Aggregation in Endogenous Network Formation Models," Papers 2310.10764, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2310.10764
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    References listed on IDEAS

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    5. Angelo Mele, 2017. "A Structural Model of Dense Network Formation," Econometrica, Econometric Society, vol. 85, pages 825-850, May.
    6. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
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