Dynamic incentives for inhibiting private sectors' opportunistic effort diversion in infrastructure PPP projects: an optimal control perspective

Purpose An optimal control model is built considering the private sector's opportunistic effort diversion and reciprocal effort improvement, while a numerical study is conducted to draw some managerial implications. Design/methodology/approach In infrastructure PPP projects, private sectors may opportunistically divert part of their effort from the current projects to other projects to allocate their limited human resources. Nevertheless, this effort diversion can be inhibited by dynamic incentives since the private sectors reciprocally exert greater effort into the current projects when receiving the dynamic incentives. This article investigates how the government specifies the output standard that the private sector should meet and offers dynamic incentives to mitigate the private sector's opportunistic effort diversion. Findings The output standard for the private sector to acquire the dynamic incentives should be specified as the output level corresponding to the private sector's optimal long-run stationary equilibrium (OLSE) effort level, which decreases with its reciprocal preference level but increases with its effort-diverting level. The optimal dynamic incentives comprise an initial incentive and a periodic OLSE incentive, which declines with the reciprocal preference level but improves with the effort-diverting level. Besides, the numerical study reveals that the government should distinguish whether the bidders have high effort-diverting levels and, if so, should focus on their reciprocal preference levels and decline the bidders with low reciprocal preference to avoid utility loss. Originality/value This article provides a theoretical model combining opportunistic behavior with reciprocal preference through an optimal control lens, thus embedding the problem of incentive design into a broader socioeconomic framework.