DISPATCH -- Decentralized Informed Spatial Planning and Assignment of Tasks for Cooperative Heterogeneous Agents

Abstract: Spatial task allocation in systems such as multi-robot delivery or ride-sharing requires balancing efficiency with fair service across tasks. Greedy assignment policies that match each agent to its highest-preference or lowest-cost task can maximize efficiency but often create inequities: some tasks receive disproportionately favorable service (e.g., shorter delays or better matches), while others face long waits or poor allocations. We study fairness in heterogeneous multi-agent systems where tasks vary in preference alignment and urgency. Most existing approaches either assume centralized coordination or largely ignore fairness under partial observability. Distinct from this prior work, we establish a connection between the Eisenberg-Gale (EG) equilibrium convex program and decentralized, partially observable multi-agent learning. Building on this connection, we develop two equilibrium-informed algorithms that integrate fairness and efficiency: (i) a multi-agent reinforcement learning (MARL) framework, EG-MARL, whose training is guided by centralized fair assignment algorithms (EG and a preference-aware Hungarian method); and (ii) a stochastic online optimization mechanism that performs guided exploration and subset-based fair assignment as tasks are discovered. We evaluate our frameworks across a range of team sizes and assignment formulations against centralized EG, Hungarian, and Min-Max Distance baselines. Both algorithms preserve the fairness-efficiency balance of the Eisenberg-Gale equilibrium under partial observability. EG-MARL achieves near-centralized coordination and reduced travel distances, while the stochastic online mechanism enables real-time allocation with competitive fairness. Together, these results demonstrate that spatially aware EG formulations can effectively guide decentralized coordination in agents with heterogeneous capabilities.