Beyond Grim: Punishment Norms in the Theory of Cooperation

The theory of repeated games asserts that, when past conduct is unobservable, the efficient outcome is attainable for any given payoff structure, if players are sufficiently patient. Here, we establish a complementary result: the efficient outcome is attainable for any degree of patience, if moving off equilibrium generates limited gains. This result builds on a class of punishment norms less extreme than “grim,” which, in fact, may be counterproductive if losses are small, as it prevents cooperation among patient players. Our analysis reveals that adoption of moderate punishment schemes can support cooper- ation when players are impatient, and provides a rationale for the empirical observation that grim punishment is uncommon in laboratory studies of cooperation.