Cooperation is vital to our survival and progress. Evolutionary game theory offers a lens to understand the structures and incentives that enable cooperation to be a successful strategy. As artificial intelligence agents become integral to human systems, the dynamics of cooperation take on unprecedented significance. Decentralized frameworks like Web3, grounded in transparency, accountability, and trust, offer a foundation for fostering cooperation by establishing enforceable rules and incentives for humans and AI agents. Guided by our Incentivized Symbiosis model, a paradigm aligning (...) human and AI agent goals through bidirectional incentives and mutual adaptation, we investigate mechanisms for embedding cooperation into human-agent coevolution. We conceptualize Incentivized Symbiosis as part of a contemporary moral framework inspired by Web3 principles, encoded in blockchain technology to define and enforce rules, incentives, and consequences for both humans and AI agents. By integrating these principles into the very architecture of human-agent interactions, Web3 ecosystems catalyze an environment ripe for collaborative innovation. Our study traverses several transformative applications of Incentivized Symbiosis, from decentralized finance to governance and cultural adaptation, illustrating how AI agents can coevolve with humans to forge a trajectory of shared, sustainable progress. (shrink)