Soft Tournament Equilibrium
Summary: arXiv:2604.04328v1 Announce Type: new
The evaluation of general-purpose artificial agents, particularly those based on large language models, presents a significant challenge due to the non-transitive nature of their interactions. When agent A defeats B, B defeats C, and C defeats A, traditional ranking methods that force a linear ordering can be misleading and unstable.
This article argues that for such cyclic domains, the fundamental object of evaluation should not be a ranking but a set-valued core, as conceptualized in classical tournament theory. This paper introduces Soft Tournament Equilibrium (STE), a differentiable framework for learning and computing set-valued tournament solutions directly from pairwise comparison data.
Key Features of Soft Tournament Equilibrium
- Probabilistic Tournament Model: STE first learns a probabilistic model of tournaments, which can be conditioned on rich contextual information.
- Differentiable Operators: The framework employs novel, differentiable operators for soft reachability and soft covering to compute continuous analogues of two seminal tournament solutions: the Top Cycle and the Uncovered Set.
- Core Agents Assessment: The output is a set of core agents, each with a calibrated membership score, providing a nuanced and robust assessment of agent capabilities.
Theoretical Foundations
The theoretical foundation for STE is developed to prove its consistency with classical solutions in the zero-temperature limit, which establishes its Condorcet-inclusion properties. The analysis extends to its stability and sample complexity, ensuring that the framework is both practical and theoretically sound.
Experimental Validation
The paper specifies an experimental protocol for validating STE on both synthetic and real-world benchmarks. This work aims to provide a complete, standalone treatise that re-centers general-agent evaluation on a more appropriate and robust theoretical foundation, moving from unstable rankings to stable, set-valued equilibria.
Conclusion
Soft Tournament Equilibrium represents a significant advancement in the evaluation of artificial agents. By shifting the focus from traditional ranking systems to a set-valued approach, STE provides a more reliable and comprehensive means of assessing agent performance in complex, cyclic interaction environments.