Honesty, Stigma, and Cooperation in an Overlapping-Generations Game

We study an overlapping-generations model of community enforcement where each agent interacts once as young and once as old across two groups. After each match a minimal, directed record assigns a public "stigma" only when a player defects against a cooperator; the label is observed solely by the defector's next partner. A known fraction of agents are honest (cooperate unless the opponent is stigmatized); the rest are strategic and privately heterogeneous in the cost of being exploited. We characterize symmetric cutoff equilibria for strategic young players. When the one-shot gain from defection is moderate, the equilibrium exists and is unique; when it is large, multiple equilibria arise. In that region, increasing the share of honest types can reduce cooperation by shifting selection toward a lower cutoff - an "honesty backfires" effect. We further show that probabilistic record-clearing weakly lowers cutoffs and never expands the cooperation region. The results yield design lessons for reputation systems: target clear opportunism and avoid mechanically forgiving records, as persistence of credible negative signals disciplines behavior across cohorts.