Helping Behavior in Large Societies

This article investigates how helping behavior can be sustained in large societies in the presence of agents who never help. I consider a game with many players who are anonymously and randomly matched every period in pairs. Within each match, one player may provide socially optimal but individually costly help to the other player. I introduce and characterize the class of “linear equilibria” in which, unlike equilibria used in the previous literature, there is help even in the presence of behavioral players. Such equilibria are close to a tit‐for‐tat strategy and feature smooth help dynamics when the society is large.