Zhu's Coalition Dynamics Model Reveals Instability-Consensus Paradox

Quanyan Zhu's latest paper, 'Multiscale Exit-Join Dynamics: Tactical Consensus and Strategic Coalition Formation,' introduces a novel framework for understanding how groups form and dissolve in multi-agent systems. The model couples two timescales: a fast 'tactical' layer where agents within a coalition reach consensus via DeGroot-style information aggregation, and a slow 'strategic' layer where agents decide to exit or join coalitions based on Aumann-Dreze payoff sharing, switching frictions, and acceptance rules. Coalition value emerges endogenously from the within-group consensus process, creating a tight feedback loop between internal agreement and external reconfiguration. The analysis characterizes joint tactical-strategic equilibria, conditions for unanimity, segregation, polarization, and cognitive barriers that sustain stable structures.

Strikingly, numerical experiments uncover an 'instability-consensus paradox': when switching barriers are low or negative, strategic convergence may never occur (coalitions keep churning), yet this very instability enables enough temporal mixing for agents across coalitions to achieve global tactical consensus. This counterintuitive result suggests that frictionless group switching can actually help spread information and align beliefs across the entire system, even as it prevents stable coalitions from forming. The paper provides existence results via fixed-point characterization and offers a unified perspective on coalition formation, consensus dynamics, and strategic stability. With applications ranging from multi-agent AI systems to political coalition theory, this work bridges game theory, information aggregation, and social dynamics.