An Entropy-Based Framework for Hybrid Coalitions in Game Theory-Part I: Human Arbitration

Area of Science:

• Artificial Intelligence
• Game Theory
• Human-AI Interaction

Background:

• Classical Game Theory is foundational for AI and multi-agent systems.
• Hybrid Human-AI systems necessitate frameworks for dynamic execution authority.
• Existing theories lack mechanisms for seamless Human-AI collaboration under algorithmic environments.

Purpose of the Study:

• Introduce Neo-Game Theory, an extension of Classical Game Theory.
• Develop a framework for hybrid Human-AI coalitions operating under Virtual Nature.
• Establish the theoretical and axiomatic basis for Human-AI collaboration with alternating authority.

Main Methods:

• Defined Neo-Game Theory integrating a lexicographic coalition utility.
• Developed a delegation rule using Jensen-Shannon divergence between Human and AI policies.
• Established agreement, contextual, and disagreement regions based on two thresholds.

Main Results:

• Introduced the first regime: Human arbitration, where AI learns via observation and frequency matching.
• AI retains final execution authority in the Human arbitration regime.
• Characterized a frequency-convergence equilibrium for the Neo-Game Theory framework.

Conclusions:

• Neo-Game Theory provides a novel framework for hybrid Human-AI systems.
• The Human arbitration regime demonstrates AI learning under human oversight.
• The established equilibrium lays the groundwork for future extensions and computational validation of Neo-Game Theory.