{"ID":2921200,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-04T00:54:56.190393508Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01663","arxiv_id":"2606.01663","title":"A Sheaf Framework for Strategic Multi-Agent Systems: From Consensus to Nash Equilibria","abstract":"The coordination of heterogeneous autonomous agents in dynamic, adversarial environments requires simultaneous satisfaction of geometric constraints, logical consistency, temporal reasoning, and strategic optimization. Existing sheaf- and topos-theoretic frameworks provide powerful tools for geometric consensus, knowledge alignment, and causal planning, but lack explicit models for value, reward, and strategic choice. This report presents a unified categorical framework that integrates event calculus, SCEL-like ensemble formation, and game-theoretic reward structures into a single Grothendieck topos of time-space histories. We introduce the notion of a \\emph{game sheaf} whose stalks contain utility functions and policy distributions, and restriction maps encode both parallel transport and best-response dynamics. We prove that Nash equilibria correspond to global sections of a derived best-response correspondence sheaf, while cohomological obstructions classify failures of strategic consistency. A detailed case study of an immunological ``bastion defense'' scenario -- heterogeneous agents forming attack/defense ensembles under resource constraints -- demonstrates the framework's expressiveness. This synthesis provides a rigorous foundation for verifiable, autonomic, and economically rational multi-agent systems.","short_abstract":"The coordination of heterogeneous autonomous agents in dynamic, adversarial environments requires simultaneous satisfaction of geometric constraints, logical consistency, temporal reasoning, and strategic optimization. Existing sheaf- and topos-theoretic frameworks provide powerful tools for geometric consensus, knowle...","url_abs":"https://arxiv.org/abs/2606.01663","url_pdf":"https://arxiv.org/pdf/2606.01663v1","authors":"[\"Manuel Hernández\",\"Eduardo Sánchez-Soto\"]","published":"2026-06-01T04:17:57Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"cs.DC\",\"cs.MA\"]","methods":"[]","has_code":false}