This paper investigates optimal contracts between risk-neutral parties when both exert efforts and the agent faces limited liability. We identify a sufficient and necessary condition for any contract to implement the second-best outcome, i.e., the best possible outcome in double moral hazard even when the agent faces unlimited liability. It is shown that a simple share-or-nothing with bonus contract (SonBo for short) is optimal and implements the second-best outcome when the condition holds. SonBo contracts have one degree of freedom, which is very useful in dealing with heterogeneous circumstances while still maintaining consistency in contracting. SonBo admits as special cases the option-like and step bonus contracts, which are widely used in dealing with limited liability. Nevertheless, we demonstrate that a step bonus contract is more powerful because an option-like contract can be problematic in some situations. The paper also discusses the performance of SonBo when the principal also faces liability constraint and investigates the optimal contract when the second-best outcome is not achievable.

本文研究了风险中立的各方在双方都付出努力并且代理商面对有限责任时的最优合同。我们为任何合同实施次优结果，即即使代理人面临无限责任的情况下，可能在双重道德风险中取得最佳结果，也确定了充分必要的条件。结果表明，简单的有分红合同的分红方案（简称“ SonBo”）是最佳的，并且在条件满足时实现次优结果。SonBo合同具有一个自由度，这在处理异构情况时非常有用，同时仍保持合同的一致性。SonBo在特殊情况下承认类期权和分步奖金合同，这些合同被广泛用于处理有限责任。尽管如此，我们证明了分步奖金合同的功能更强大，因为类似期权的合同在某些情况下可能会出现问题。本文还讨论了当委托人也面临责任约束时SonBo的表现，并研究了无法获得次优结果时的最优合同。