  We study binary coordination games with random utility played in networks. A
typical equilibrium is fuzzy -- it has positive fractions of agents playing
each action. The set of average behaviors that may arise in an equilibrium
typically depends on the network. The largest set (in the set inclusion sense)
is achieved by a network that consists of a large number of copies of a large
complete graph. The smallest set (in the set inclusion sense) is achieved on a
lattice-type network. It consists of a single outcome that corresponds to a
novel version of risk dominance that is appropriate for games with random
utility.
