[2603.11560] Theory of Dynamic Adaptive Coordination

Computer Science > Multiagent Systems arXiv:2603.11560 (cs) [Submitted on 12 Mar 2026 (v1), last revised 26 Mar 2026 (this version, v2)] Title:Theory of Dynamic Adaptive Coordination Authors:Stefano Grassi View a PDF of the paper titled Theory of Dynamic Adaptive Coordination, by Stefano Grassi View PDF Abstract:This paper develops a dynamical theory of adaptive coordination governed by persistent environmental memory. Moving beyond framework-specific equilibrium optimization or agent-centric learning, I model agents, incentives, and the environment as a recursively closed feedback architecture: a persistent environment stores accumulated coordination signals, a distributed incentive field transmits them locally, and adaptive agents update in response. Coordination thus emerges as a structural consequence of dissipative balancing against reactive feedback, rather than the solution to a centralized objective. I establish three primary results. First, I show that under dissipativity, the closed-loop system admits a bounded forward-invariant region, ensuring viability independent of global optimality. Second, I demonstrate that when incentives hinge on persistent memory, coordination becomes irreducible to static optimization. Finally, I identify the essential structural condition for emergence: a bidirectional coupling where memory-dependent incentives drive agent updates, which in turn reshape the environmental state. Numerical verification identifies a Neimark-Sacker bifur...