Compensation contracts for multiple agents with helping effort under bilateral moral hazard

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.