The construction industry often relies on subcontracting, where subcontractors bid for portions of a project before general contractors bid for the entire project in a process referred to as multi-stage bidding (MSG). MSG can be complex, and winning bidders may be burdened with underestimating their bids and encountering the winner's curse. Despite various studies investigating this issue, further research is necessary to examine bidding strategies for subcontractors. This paper addresses this research need by exploring and comparing how bidding strategies based on reinforcement learning and game theory could aid subcontractors in mitigating the winner's curse in MSG. The authors used a multi-step research methodology comprised of (1) formulating an MSG framework; (2) incorporating MSG game-theoretic bid function as the adopted game theory-based strategy, and modified Roth-Erev algorithm as the adopted reinforcement learning-based strategy; and (3) comparing the results of the two bidding strategies using an MSG simulation model. Results revealed that the reinforcement learning-based bidding strategy was more effective in mitigating the winner's curse for the subcontractors in MSG compared to the game theory-based bidding strategy. Ultimately, this research may improve subcontractors' pricing practices and support them in managing the complexities and uncertainties inherent in MSG decision-making.