The growing integration of distributed energy resources drives the centralized power system towards a decentralized multi-agent network. Operating multi-agent networks significantly relies on inter-agent communications. Computation granularity in this context refers to the number of nodes overseen by an agent. The impact of granularity on equitable power coordination, particularly among marginalized customers with limited communication bandwidth (e.g., intermittent internet connectivity) is not well studied. This work explores different levels of computation granularity for agent-based energy dispatch and studies their impact on equitable coordination. We will leverage and utilize the Consensus + Innovations approach to model the equitable coordination of a multi-agent power system.