Reactive path planning to avoid collisions with moving obstacles enables more robust agent systems. However, many solutions assume that moving objects are passive; that is, they do not consider that the moving objects are themselves re-planning to avoid collisions, and thus may change their trajectory. In this paper we present a model, Anticipatory Stigmergic Collision Avoidance (ASCA) for reciprocal collision avoidance using anticipatory stigmergy. Unlike standard stigmergy, in which agents leave pheromones to indicate a trace of previous actions, anticipatory stigmergy deposits pheromones on intended future paths. By sharing their intended future paths with each other at regular intervals, agents can re-plan to attempt to avoid collisions. We experimentally evaluate ASCA over three scenarios, and compare with a state of art approach, Reciprocal Velocity Obstacles (RVO). Our evaluation showed that ASCA is consistently more robust in noisy environments in which transmitted information can be lost or degraded. Further, using ASCA without noise results in fewer collisions than RVO when agents are in formation, but more collisions when formed randomly.