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

TL;DR

This paper develops a game-theoretic framework for GenAI acting as digital representatives in subjective, collective decision-making, where members strategically reveal information to the AI. It introduces a prior-driven learning model with a convex communication cost and derives closed-form Nash equilibria, showing that members with conflicting preferences reveal more information than aligned ones. Through theoretical and numerical analyses, the authors compare digital representatives to direct participation, finding that digital proxies can closely approximate manual decisions under high manual costs or advanced GenAI, while never perfectly representing individual preferences. The results offer practical guidance on deploying GenAI in collaborative tasks and lay a foundation for extending the model to larger teams and privacy-aware settings.

Abstract

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.

Figures (8)

• Figure 1: Illustration of the digital representative game.
• Figure 2: Illustration of two-member Nash equilibrium: No revelation (green), one-member revelation (yellow for Alice, blue for Bob), and both members revealing with aligned (red) or conflicting (purple) preferences.
• Figure 3: Illustration of Nash Equilibrium.
• Figure 4: Comparison of Team Decision.
• Figure 5: Comparison of Team Preference Loss.

Theorems & Definitions (9)

• Definition 1: Digital Representative Game
• Definition 2: Alice's Best Response
• Proposition 1: Best Response of Digital Representative Game
• Definition 3: Nash Equilibrium
• Theorem 2: Nash Equilibrium of Digital Representative Game
• Proposition 3: OPR Equilibrium Properties
• Proposition 4: BPR Equilibrium Properties
• Proposition 5: Diversity and Revelation
• Theorem 6: Equilibrium versus Baseline Team Outcomes