  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.
