Avoidance and Mitigation of Public Harm

This paper studies the optimal design of a liability sharing arrangement as an infinitely repeated game. We construct a schematic, non-cooperative, 2-player model where an active agent can take a costly, unobservable action to try to avert a crisis, and then when a crisis occurs, both agents decide how much to contribute mitigating it. The model is able to generate any combination of avoidance/mitigation patterns as static Nash equilibrium. We then consider perfect public equilibrium (PPE) of the infinitely repeated game. When the avoidance cost is higher than the expected loss of crisis for the active agent, the first best is not a static Nash equilibrium of the stage game and cannot be implemented as a PPE of the repeated game. For this case we find a PPE that dominates the repetition of the static Nash. At this equilibrium, the frequency of the active agent taking the costly avoidance action is endogenously determined, hence the equilibrium crisis rate is also endogenously determined. In the period when no action is taken and crisis occurs, the passive agent "bails out" the active agent by paying more than his share of the mitigation cost.