We consider a model where each individual (or ethnic minority) is embedded in a network of relationships and decides whether or not she wants to be assimilated to the majority norm. Each individual wants her behavior to agree with her personal ideal action or norm but also wants her behavior to be as close as possible to the average assimilation behavior of her peers. We show that there is always convergence to a steady-state and characterize it. We also show that different assimilation norms may emerge in steady state depending on the structure of the network. We then consider the role of cultural and government leaders in the assimilation process of ethnic minorities and an optimal tax/subsidy policy which aim is to reach a certain level of assimilation in the population.