Modeling conflicting incentives in engineering senior capstone projects: A multi-player game theory approach

University engineering capstone projects involve sustained interaction among students, faculty, and industry sponsors whose objectives are only partially aligned. While capstones are widely used in engineering education, existing analyses typically treat stakeholder behavior informally or descriptively, leaving incentive conflicts, information asymmetries, and strategic dependencies underexplored. This paper develops a formal game-theoretic framework that models capstone projects as a sequential Bayesian game involving three players: the university, the industry sponsor, and the student team. The framework is intended as an analytical and explanatory tool for understanding how institutional policy choices, such as grading structures, intellectual property rules, and sponsor engagement expectations, shape stakeholder behavior and project outcomes, rather than as a calibrated or predictive model. The university acts as a constrained Stackelberg leader by committing to course policies and assessment structures while anticipating strategic responses by sponsors and students under incomplete information. Reduced-form outcome functions capture technical quality, documentation quality, timeliness, alignment with sponsor needs, and publishability, while payoff functions reflect stakeholder-specific objectives and costs. Under standard assumptions, the model admits stable equilibrium regimes that correspond to empirically recognizable capstone dynamics observed in practice, including cooperative engagement, sponsor-dominated exploitation, and student grade gaming. Rather than claiming precise prediction, the framework provides a structured basis for reasoning about incentive design, policy tradeoffs, and structural failure modes in project-based learning environments, as well as for future extensions incorporating richer dynamics, repeated interaction, and empirical calibration.