Fuzzy Conventions , 2022 , Slides
We propose an equilibrium selection theory for Granovetter (1978)’s threshold adoption model on networks. In the model, each agent adopts a new behavior only if the fraction of her neighbors doing the same is larger than her i.i.d. threshold. A fuzzy convention y is a profile where, for (almost) all agents, approximately y fraction of their neighbors adopts a new behavior. A random-utility (RU) dominant outcome x is a maximizer of an integral of the distribution of thresholds. The definition generalizes Harsanyi and Selten (1988)’s risk dominance to coordination games with random utility. We show that each network, if the number of agents is large and each agent has sufficiently many neighbors, has a fuzzy convention x. On some networks, including a city network, all equilibria are fuzzy conventions x. Fuzzy convention x is the only profile with such properties, and the only profile robust to incomplete information about the network structure.