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We propose an extension to the MAPF formulation, called SocialMAPF, toaccount for private incentives of agents in constrained environments such asdoorways, narrow hallways, and corridor intersections. SocialMAPF is able to,for instance, accurately reason about the urgent incentive of an agent rushingto the hospital over another agent's less urgent incentive of going to agrocery store; MAPF ignores such agent-specific incentives. Our proposedformulation addresses the open problem of optimal and efficient path planningfor agents with private incentives. To solve SocialMAPF, we propose a new classof algorithms that use mechanism design during conflict resolution tosimultaneously optimize agents' private local utilities and the global systemobjective. We perform an extensive array of experiments that show that optimalsearch-based MAPF techniques lead to collisions and increased time-to-goal inSocialMAPF compared to our proposed method using mechanism design. Furthermore,we empirically demonstrate that mechanism design results in models thatmaximizes agent utility and minimizes the overall time-to-goal of the entiresystem. We further showcase the capabilities of mechanism design-based planningby successfully deploying it in environments with static obstacles. Toconclude, we briefly list several research directions using the SocialMAPFformulation, such as exploring motion planning in the continuous domain foragents with private incentives.

SOCIALMAPF: Optimal and Efficient Multi-Agent Path Finding with Strategic Agents for Social Navigation