A model of the formation of multilayer networks

• 成果类型: Article
• 署名作者: Billand, Pascal; Bravard, Christophe; Joshi, Sumit; Mahmud, Ahmed Saber; Sarangi, Sudipta
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Lyon 2; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); George Washington University; Virginia Polytechnic Institute & State University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2023.105718
• 发表日期: 2023
• 关键词: Multilayer networks; concavity; convexity; supermodularity; Submodularity

摘要

We study the formation of multilayer networks where payoffs are determined by the degrees of players in each network. We begin by imposing either concavity or convexity in degree on the payoff function of the players. We then explore distinct network relationships that result from inter- and intra-network spillovers captured by the properties of supermodularity/submodularity and strategic complementarity respectively. We show the existence of equilibria and characterize them. Additionally, we establish both necessary and sufficient conditions for an equilibrium to occur. We also highlight the connection, in equilibrium, between inter-network externalities and the identity of linked players in one network given the identity of linked players in the other network. Furthermore, we analyze efficient multilayer networks. Finally, we extend our models to contexts with more than two layers, and scenarios where agents receive a bonus for being connected to the same individuals in both networks.