Free Love , Fragile Fidelity , and Forgiveness : Rival Social Conventions under Hidden Information

Social conventions can foster cooperation in relationships even if each partner can break the relationship at any time and get a fresh start. We consider settings where the underlying problem is hidden information (rather than moral hazard). Agents’ instantaneous payoffs are private information and change from period to period. We identify optimal strongly-symmetric social conventions. One of just two rules on what to do if cheating occurs is always optimal: a draconian ‘fragile-fidelity’ rule (break up the relationship whenever either party cheats); and a more forgiving ‘christmas-card’ rule (only break up if both parties cheat in the same period). These rules are simple, and resemble those found in reality. The conditions for each to be optimal match the intuition suggested by the names. We fully characterize the optimal equilibrium paths. The probability that a relationship will break up in a given period decreases with duration, but, even in old relationships, cheating and break ups occur on the equilibrium path. Given underlying parameters, we can predict the induced distribution of relationship lengths that will be observed.