Addressing the challenges of insufficient incentives, weak constraints, and superficial adoption in promoting human–robot collaboration (HRC) in the construction industry, this study develops a tripartite evolutionary game model among government, contractors, and on-site teams under bounded rationality. Lyapunov stability analysis and numerical simulation are employed to conduct parameter sensitivity analyses. The results show that a strategy profile characterized by flexible regulation, deep adoption, and high-effort collaboration constitutes a stable evolutionary outcome. Moderately increasing government incentives helps accelerate convergence but exhibits diminishing returns under fiscal constraints, indicating that subsidies alone cannot sustain genuine engagement. Reducing penalties for contractors and on-site teams, respectively, induces superficial adoption and low effort, whereas strengthening penalties for bilateral violations simultaneously compresses the space for opportunistic behavior. When the payoff advantage of deep adoption narrows or the payoff from perfunctory adoption rises, convergence toward the preferred steady state slows markedly. Based on the discussion and simulation evidence, we recommend dynamically matching incentives, sanctions, and performance feedback: prioritizing flexible regulation to reduce institutional frictions, configuring differentiated sanctions to maintain a positive payoff differential, reinforcing observable performance to stabilize frontline effort, and adjusting policy weights by project stage and actor characteristics. The study delineates how parameter changes propagate through behavioral choices to shape collaborative performance, providing actionable guidance for policy design and project governance in advancing HRC.