The success of deployed agents relies on their ability to handle open-ended user requests using their inherent capabilities, not only in solving requests directly but also in effectively leveraging inter-agent communication channels and feedback signals over time. This requires a multi-agent environment where agents can operate autonomously, strategically communicate, behave collaboratively and be driven by economic incentives, much like humans in society. Towards this vision, we propose $\mathtt{AgentSociety}$, a mechanism that enables decentralized agentic collaboration grounded in liquid democracy and information diffusion from social choice theory. We show that $\mathtt{AgentSociety}$ provides an environment for agents to make autonomous decisions utilizing their local context to maximize their utility while achieving collective outcomes through incentivized collaboration. Specifically, we prove that delegation to more competent neighbor agents is incentive compatible and naturally generates multi-agent routing path by consensus. Additionally, our mechanism incentivizes agents to selectively disclose information to their neighbor agents when doing so aligns with their self-interest, so as to garner influence. We characterize the Nash equilibrium showing that agent payoffs are reflective of their marginal contributions. We compare and benchmark strategy profiles adopted by open and proprietary state-of-the-art language models deployed in $\mathtt{AgentSociety}$ against best response. Finally, we evaluate collaborative performance from consensus-based routing among self-interested heterogeneous agents in $\mathtt{AgentSociety}$ on real-world datasets.