Building social networks under consent: A survey

TL;DR

This survey reviews game-theoretic models of social network formation under mutual consent, highlighting the challenges and solutions for achieving non-trivial networks through various equilibrium concepts and rationality assumptions.

Contribution

It provides a comprehensive overview of non-cooperative approaches and refinements to model network formation with mutual consent, including new stability notions and external correlation devices.

Findings

Empty network is a strong Nash equilibrium under mutual consent.

Pairwise stability requires coordinated decision-making.

Unilateral and monadic stability offer alternative explanations for non-trivial networks.

Abstract

This survey explores the literature on game-theoretic models of network formation under the hypothesis of mutual consent in link formation. The introduction of consent in link formation imposes a coordination problem in the network formation process. This survey explores the conclusions from this theory and the various methodologies to avoid the main pitfalls. The main insight originates from Myerson's work on mutual consent in link formation and his main conclusion that the empty network (the network without any links) always emerges as a strong Nash equilibrium in any game-theoretic model of network formation under mutual consent and positive link formation costs. Jackson and Wolinsky introduced a cooperative framework to avoid this main pitfall. They devised the notion of a pairwise stable network to arrive at equilibrium networks that are mainly non-trivial. Unfortunately, this notion of pairwise stability requires coordinated action by pairs of decision makers in link formation. I survey the possible solutions in a purely non-cooperative framework of network formation under mutual consent by exploring potential refinements of the standard Nash equilibrium concept to explain the emergence of non-trivial networks. This includes the notions of unilateral and monadic stability. The first one is founded on advanced rational reasoning of individuals about how others would respond to one's efforts to modify the network. The latter incorporates trusting, boundedly rational behaviour into the network formation process. The survey is concluded with an initial exploration of external correlation devices as an alternative framework to address mutual consent in network formation.