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In this article we study the theoretical aspects of the collision avoidance among the collectives of unmanned aerial vehicles (UAVs) engaged in the free flight operation. The free flight based operations do not provide collision-free trajectories as a flight specification to the UAVs. Collision avoidance of the trajectories is implemented by means of peer-to-peer negotiations among the individual UAVs. In this paper we study the role of interaction in the collision avoidance process. We prove theoretically convergence of the specific negotiating protocol that has been deployed in a practical implementation of the software prototype of the distributed collision avoidance system.