Contagion

Each player in an infinite population interacts strategically with a finite subset of that population. Suppose each player's binary choice in each per iod is a best response to the population choices of the previous period. Wh en can behaviour that is initially played by only a finite set of players s pread to the whole population? This paper characterizes when such contagion is possible for arbitrary local interaction systems. Maximal contagion occ urs when local interaction is sufficiently uniform and there is low neighbo ur growth, i.e. the number of players who can be reached in k steps does no t grow exponentially in k.