  We propose an extension to the MAPF formulation, called SocialMAPF, to
account for private incentives of agents in constrained environments such as
doorways, narrow hallways, and corridor intersections. SocialMAPF is able to,
for instance, accurately reason about the urgent incentive of an agent rushing
to the hospital over another agent's less urgent incentive of going to a
grocery store; MAPF ignores such agent-specific incentives. Our proposed
formulation addresses the open problem of optimal and efficient path planning
for agents with private incentives. To solve SocialMAPF, we propose a new class
of algorithms that use mechanism design during conflict resolution to
simultaneously optimize agents' private local utilities and the global system
objective. We perform an extensive array of experiments that show that optimal
search-based MAPF techniques lead to collisions and increased time-to-goal in
SocialMAPF compared to our proposed method using mechanism design. Furthermore,
we empirically demonstrate that mechanism design results in models that
maximizes agent utility and minimizes the overall time-to-goal of the entire
system. We further showcase the capabilities of mechanism design-based planning
by successfully deploying it in environments with static obstacles. To
conclude, we briefly list several research directions using the SocialMAPF
formulation, such as exploring motion planning in the continuous domain for
agents with private incentives.
