A Differential Game Analysis on Government–Firm Collaboration in Emergency Construction: From Perspective of Goodwill

The successful delivery of emergency construction depends on efficient government–firm collaboration, yet the high risks and costs challenge the construction firm’s motivation to invest in construction efforts. This study develops a differential game model to investigate the effort decisions of the government and construction firms through positioning firm goodwill as a dynamic motivation. The model further introduces the delay effects of construction effort to investigate the optimal decision-making approach (decentralized, cost-sharing, or centralized) between the government and construction firms. The findings are as follows. First, this study reveals a critical asymmetry in delay effects: although delays are fundamentally detrimental to profits and goodwill, the model shows that the construction firm’s delay is more damaging to both profits and goodwill than the government’s. Second, no single decision-making approach is universally dominant; the optimal choice is contingent on the strategic objective. The centralized approach is consistently optimal for maximizing total government–firm profits. However, the cost-sharing approach is superior for maximizing goodwill and becomes the most effective for sustaining the firm’s effort as delay effects increase. Theoretically, this study provides a new perspective that treats goodwill as a strategic asset and identifies the influence of delay effects on decision-making approaches. Practically, the findings guide firms to actively manage their goodwill and urge the government and firms to select the optimal collaboration approach.