On payoff heterogeneity in games with strategic complementarities

Recent papers involving binary choices have argued that increasing heterogeneity decreases positive feedback. We show that no such result holds in models where all agents make interior choices. The results in the binary choice case arise for two reasons. First, if we increase heterogeneity without limit but impose a bounded choice set, then almost all players eventually become completely unresponsive, preferring some corner so strongly that they do not react to any feasible change in the behavior of others. Second, discrete choice permits the construction of strong, but fragile, positive feedbacks through composition effects.