This paper aims to investigate the compensation contract design problem consisting of a risk neutral firm and two risk averse workers with and without helping effort in the presence of bilateral moral hazard by Stackelberg game in the framework of principal-agent theory. Three classes of contract models are established in three modes, which reflect whether helping effort takes place between both workers and whether personal performance evaluation contract or relative performance evaluation contract is applied by the firm. By solving models, optimal efforts of the firm, optimal individual and workgroup incentive coefficients, optimal personal effort and helping effort, and the firm’s expected profit are deduced in different modes. In addition, a numerical experiment is investigated by focusing on the impacts of effort cost coefficients of the firm and the worker, and bilateral moral hazard on optimal compensation contracts and profit of the firm in three modes, which provide some valuable management insights about optimal strategy for the firm. The main findings show that the relative performance evaluation contract works better than the personal performance evaluation contract when the two workers is cooperative, which means that helping effort takes place between the two workers. Furthermore, a higher marginal contribution can motive the worker to make more helping effort for her partner, thus achieving win-win outcome based on the relationship of cooperation. For the firm, the optimal strategy is to design the relative performance evaluation contract for both workers and motivate them to make cooperative relationship by exerting helping effort under bilateral moral hazard. Moreover, bilateral moral hazard decreases the motivations of the workers but increases the firm’s profit. This proposed work contributes to the investigation of compensation contract design by combining three critical factors, that is, multiple agents, bilateral moral hazard, and helping effort. The findings provide some theoretical guidance on how to set up optimal mechanism between the firm and multiple agents in the presence of bilateral moral hazard and how to reduce the adverse influence of bilateral moral hazard on participants’ profits.

中文翻译：

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双边道德风险下多方代办的补偿合同

本文旨在在委托代理理论的框架下，通过Stackelberg博弈研究由双方风险中立的公司和两名厌恶风险的工人组成的补偿合同设计问题。在三种模式下建立了三类合同模型，分别反映了两个员工之间是否都在努力工作，以及公司是否采用了个人绩效评估合同或相对绩效评估合同。通过求解模型，可以用不同的方式推导企业的最佳努力，最佳的个人和工作组激励系数，最佳的个人努力和帮助努力以及企业的预期利润。此外，通过关注企业和工人的劳动成本系数，双边道德风险对企业最优补偿合同和企业利润的三种方式的影响进行了数值实验，为企业最优战略提供了有价值的管理见解。主要研究结果表明，当两个工人合作时，相对绩效评估合同要比个人绩效评估合同更好，这意味着两个工人之间需要进行帮助。此外，更高的边际贡献可以激励工人为伴侣提​​供更多的帮助，从而在合作关系的基础上实现双赢。对于公司 最佳策略是为双方员工设计相对绩效评估合同，并通过在双边道德风险下进行帮助而激励他们建立合作关系。而且，双边道德风险降低了工人的动力，但增加了公司的利润。这项拟议的工作通过结合三个关键因素，即多重行为人，双边道德风险和帮助努力，为赔偿合同设计的研究做出了贡献。研究结果为在存在双边道德风险的情况下如何建立企业与多重主体之间的最优机制以及如何减少双边道德风险对参与者利润的不利影响提供了理论指导。双边道德风险降低了工人的动力，但增加了公司的利润。这项拟议的工作通过结合三个关键因素，即多重行为人，双边道德风险和帮助努力，为赔偿合同设计的研究做出了贡献。研究结果为在存在双边道德风险的情况下如何建立企业与多重主体之间的最优机制以及如何减少双边道德风险对参与者利润的不利影响提供了理论指导。双边道德风险降低了工人的动力，但增加了公司的利润。这项拟议的工作通过结合三个关键因素，即多重行为人，双边道德风险和帮助努力，为赔偿合同设计的研究做出了贡献。研究结果为在存在双边道德风险的情况下如何建立企业与多重主体之间的最优机制以及如何减少双边道德风险对参与者利润的不利影响提供了理论指导。