Open AccessA model of weighted network formation
Author(s) -
Baumann Leonie
Publication year - 2021
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2177
Subject(s) - reciprocal , pairwise comparison , network formation , mathematical economics , link (geometry) , microeconomics , graph , externality , computer science , economics , artificial intelligence , theoretical computer science , computer network , philosophy , linguistics , world wide web
This paper proposes a game of weighted network formation in which each agent has a limited resource to form links of possibly different intensities with other agents and to use for private purposes. We show that every equilibrium is either “reciprocal” or “nonreciprocal.” In a reciprocal equilibrium, any two agents invest equally in the link between them. In a nonreciprocal equilibrium, agents are partitioned into “concentrated” and “diversified” agents, and a concentrated agent is only linked to diversified agents and vice versa. For every link, the concentrated agent invests more in the link than the diversified agent. The unweighted relationship graph of an equilibrium, in which two agents are linked if they both invest positively in each other, uniquely predicts the equilibrium values of each agent's network investment and utility level, as well as the ratio of any two agents' investments in each other. We show that equilibria are not pairwise stable and are not efficient due to the positive externalities of investing in a link.