Abstract. We study static binary coordination games with random utility played on networks. In equilibrium, each agent chooses an action only if a fraction of her neighbors choosing the same action is higher than an agent-specific i.i.d. threshold. A fuzzy convention x is a profile where (almost) all agents choose the high action if their threshold is smaller than x and the low action otherwise. The random-utility (RU) dominant outcome x^{*} is a maximizer of an integral of the distribution of thresholds. The definition generalizes Harsanyi-Selten's risk dominance to coordination games with random utility. We show that, on each sufficiently large and fine network, there is an equilibrium that is a fuzzy convention x^{*}. On some networks, including a city network, all equilibria are fuzzy conventions x^{*}. Finally, fuzzy conventions x^{*} are the only behavior that is robust to misspecification of the network structure.