Provocable Forgiveness in Noisy Brand--Consumer Systems:An Agent-Based Study of Repeated Interaction

Repeated brand--consumer exchange is often treated as a managerial problem of loyalty, recovery, and trust. It can also be read as a small complex system: many local decisions about cooperation, retaliation, and forgiveness accumulate into market-level selection. This study uses that perspective to examine which relational rules survive when communication is imperfect. Eight canonical Iterated Prisoner's Dilemma strategies are translated into marketing archetypes and evaluated through round-robin tournaments, a six-level noise sweep, proportional-fitness ecological dynamics, and finite-population Moran invasion tests. The tournament leaderboard is calculated without same-strategy self-play, so that reported payoffs reflect inter-archetype competition rather than homogeneous self-coordination. At a 5\% noise level, a Vindictive Brand and an Opportunist Brand achieve the highest fixed-population payoffs; the Loyalist Brand, by contrast, loses 24.4\% of its noiseless value. When the population is allowed to evolve, the interpretation changes. By generation 200, forgiving and patient strategies dominate the surviving ecology, while vindictive and opportunistic strategies have vanished. Moran tests against a Reciprocator incumbent tell the same cautionary story: exploitative invaders fixate far less often than reciprocal, forgiving, or pragmatic invaders. The mechanism is a timescale effect. Provocability protects a brand against exploitation in the short run, but forgiveness is what repairs cooperation after ordinary noise. The paper contributes a reproducible agent-based framework for studying relational strategy in noisy markets and develops the managerial principle of \emph{provocable forgiveness} for service recovery, loyalty design, and algorithmic customer management.