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Theoretical determination of the exact phase-transition point in DRLP-MG

Determine the exact phase-transition point in the Dual Reinforcement Learning Policies Minority Game (DRLP-MG) through a theoretical analysis that overcomes the heterogeneity of agents’ Q-tables, which prevents direct application of existing dimensionality-reduction approaches.

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Background

The paper reports a first-order phase transition in volatility with respect to the fraction of classical-policy agents and provides empirical and semi-analytical characterizations, but it does not pinpoint the transition point analytically.

The authors explain that standard dimensionality reduction methods used in related work are not directly applicable due to the heterogeneity of agents’ Q-tables, leaving the precise theoretical identification of the transition point unresolved.

References

Our research has shown that reinforcement policies with different learning granularities can form synergistic effects in resource allocation through the momentum strategy, yet several open questions remain. Secondly, the heterogeneity of the agent’s Q - table makes it nearly impossible to use previous work for dimensionality reduction analysis and theoretically determine the exact phase-transition point.

— Dual Reinforcement Learning Synergy in Resource Allocation: Emergence of Self-Organized Momentum Strategy (2509.11161 - Zhang et al., 14 Sep 2025) in Section 5 (Discussion and Conclusion)