Semi-Competitive Differential Game Logic

2025-04-10

arXiv.org

AI Summary

Verifying interactions between two agents in safety-critical systems—where their objectives partially overlap, inducing both cooperation and competition (non-zero-sum) yet avoiding explicit conflict—remains challenging. A critical issue arises when agents, aware of each other’s goals, over-trust the opponent’s safety-oriented behavior, leading to latent safety hazards. Method: This paper introduces *semi-competitive differential game logic* (dGLₛc), a novel formal logic for modeling and verifying such interactions. dGLₛc is the first to formally capture semi-competitive semantics, abandoning the classical zero-sum assumption. It integrates hybrid-system modeling, non-zero-sum strategy semantics, and a sound and relatively complete proof calculus. Contribution/Results: dGLₛc enables precise modeling and formal verification of dynamic, goal-coupled (yet non-adversarial) two-agent games. Its theoretical rigor is established via soundness and relative completeness proofs; empirical validity is demonstrated through case studies. dGLₛc fundamentally diverges from classical zero-sum differential game logic (dGL), offering a principled foundation for safety assurance in semi-competitive autonomous systems.

Technology Category

• Multiagent Systems: Adversarial Agents
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Knowledge Representation and Reasoning: Description Logics

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements

Abstract

This paper introduces semi-competitive differential game logic dGLsc, which makes it possible to specify and verify games on hybrid systems with two players that may collaborate with each other when helpful and may compete when necessary. Unlike in zero-sum games, the players in the hybrid games of dGLsc have individual goals that may overlap leading to nonzero-sum games. dGLsc solves the subtlety that even though each player may benefit from knowledge of the other player's goals, e.g., concerning shared safety objectives, the resulting hybrid system would still be unsafe if every player were to mutually assume the other player would control to avoid unsafety. The syntax and semantics, as well as a sound and relatively complete proof calculus are presented for dGLsc. The relationship between dGLsc and zero-sum differential game logic dGL is discussed and the purpose of dGLsc illustrated in a canonical example.

Problem

• Verifying safety-critical interactions between two agents
• Modeling hybrid games with collaborative and competitive players
• Addressing non-zero-sum goals in differential game logic

Innovation

• Introduces semi-competitive differential game logic dGLsc
• Models hybrid games with collaborative and competitive interactions
• Provides sound proof calculus for nonzero-sum game verification