This paper presents our on-going research into selforganizing and self-healing networks of resource brokers, for use in complex Peer-to-Peer (P2P) resource sharing and Grid computing application environments. It discusses our objectives for an efficient, robust, and decentrally controlled infrastructure, and describes our efforts to understand the co-dependencies between protocols, topologies, and continuously changing environmental conditions. Motivated by dynamic social and economic systems, our research project is nicknamed AESOP, for Adaptive Economic Society Of Peers. We discuss our specific investigations into adaptive topologies for flooding-based distributed search protocols, Genetic Algorithm explorations seeking good topological structures, and current work to develop an agent-based simulation to investigate the effects of peer transience on P2P join and topology maintenance protocols.