A Crises-Bailouts Game

This paper studies the optimal design of a liability-sharing arrangement as an infinitely repeated game. We construct a noncooperative model with an active and a passive agent. The active agent can take a costly and unobservable avoidance action to reduce the incidence of a crisis, but a crisis is costly for both agents. When a crisis occurs, each agent decides how much to contribute to mitigating it. For the one-shot game, when the avoidance cost is not too high relative to the expected loss of crisis for the active agent, a no-bailout policy always achieves the first-best outcome, at which the active agent puts in effort to minimize the crisis incidence. However, the first-best is not achievable when the avoidance cost is sufficiently high. We show that, in the latter case with the same stage game, the first-best cannot be implemented as a perfect public equilibrium (PPE) of the infinitely repeated game either. Instead, at any constrained efficient PPE with avoidance, the active agent “shirks” infinitely often, though crises are always mitigated, and is bailed out infinitely often. The reason is that promises of future shirking and bailout incentivize the active player to take the costly crisis-avoidance action in the present. This result runs contrary to the typical moral hazard view that bailouts reduce incentives for agents to avoid crises. Here bailouts enhance ex-ante mitigation efforts rather than diminish them and are necessary to achieve the second-best. We use finite-state automata to approximate the constrained efficient PPE and explore some comparative statics of the repeated game numerically.