Generative AI as Digital Representatives in Collective Decision-Making: A Game-Theoretical Approach

Generative Artificial Intelligence (GenAI) enables digital representatives to make decisions on behalf of team members in collaborative tasks, but faces challenges in accurately representing preferences. While supplying GenAI with detailed personal information improves representation fidelity, feasibility constraints make complete information access impractical. We bridge this gap by developing a game-theoretic framework that models strategic information revelation to GenAI in collective decision-making. The technical challenges lie in characterizing members' equilibrium behaviors under interdependent strategies and quantifying the imperfect preference learning outcomes by digital representatives. Our contribution includes closed-form equilibrium characterizations that reveal how members strategically balance team decision preference against communication costs. Our analysis yields an interesting finding: Conflicting preferences between team members drive competitive information revelation, with members revealing more information than those with aligned preferences. While digital representatives produce aggregate preference losses no smaller than direct participation, individual members may paradoxically achieve decisions more closely aligned with their preferences when using digital representatives, particularly when manual participation costs are high or when GenAI systems are sufficiently advanced.