Random utility coordination games on networks

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.