Continuous Optimisation Problem and Game Theory for Multi-Agent Pathfinding

In the article, we studied the continuous problem for multi-agent pathfinding. We show continuity of the path-traversing time functional and the existence of the optimal path for a single agent. Also, we consider game theory interpretation for multi-agent pathfinding with continuous routes as a game with strategies in a Banach space. Finally, we briefly discuss near-optimal routes and connection of heuristics for pathfinding and integral geometry problems.