The ongoing shift of AI models from centralized cloud APIs to local AI agents on edge devices is enabling \textit{Client-Side Autonomous Agents (CSAAs)} -- persistent personal agents that can plan, access local context, and invoke tools on behalf of users. As these agents begin to collaborate by delegating subtasks directly between clients, they naturally form \emph{Agentic Peer-to-Peer (P2P) Networks}. Unlike classic file-sharing overlays where the exchanged object is static, hash-indexed content (e.g., files in BitTorrent), agentic overlays exchange \emph{capabilities and actions} that are heterogeneous, state-dependent, and potentially unsafe if delegated to untrusted peers. This article outlines the networking foundations needed to make such collaboration practical. We propose a plane-based reference architecture that decouples connectivity/identity, semantic discovery, and execution. Besides, we introduce signed, soft-state capability descriptors to support intent- and constraint-aware discovery. To cope with adversarial settings, we further present a \textit{tiered verification} spectrum: Tier~1 relies on reputation signals, Tier~2 applies lightweight canary challenge-response with fallback selection, and Tier~3 requires evidence packages such as signed tool receipts/traces (and, when applicable, attestation). Using a discrete-event simulator that models registry-based discovery, Sybil-style index poisoning, and capability drift, we show that tiered verification substantially improves end-to-end workflow success while keeping discovery latency near-constant and control-plane overhead modest.