“Contagion and Uninvadability in Social Networks with Bilingual Option” by Satoru Takahashi
University of Tokyo
We study the long run outcome of local interactions in an infinite population of players, each of whom chooses one of two conventions or adopts both (i.e., chooses the “bilingual option”) at an additional cost. In this class of games, we completely characterize when a convention spreads contagiously from a finite subset of players to the entire population in some network, and conversely, when a convention is never invaded by the other convention in any network. Generically, at least one convention spreads contagiously in some network, and for some range of payoff parameters, both conventions each spread contagiously in respective networks. Our proofs for this characterization provide new insights on how the network structure affects contagion.