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We present a navigation planning framework for dynamic, multi-agent environments, where no explicit communication takes place among agents. Inspired by the collaborative nature of human navigation, our approach encodes the concept of coordination into an agent's decision making through an inference mechanism about collaborative strategies of collision avoidance. Each such strategy represents a distinct avoidance protocol, prescribing a distinct class of navigation behaviors to agents. We model such classes as equivalence classes of multi-agent path topology, using the formalism of topological braids. This formalism may naturally encode any arbitrarily complex, spatiotemporal, multi-agent behavior, in any environment with any number of agents into a compact representation of dual algebraic and geometric nature. This enables us to construct a probabilistic inference mechanism that predicts the collective strategy of avoidance among multiple agents, based on observation of agents' past behaviors. We incorporate this mechanism into an online planner that enables an agent to understand a multi-agent scene and determine an action that not only contributes progress towards its destination, but also reduction of the uncertainty of other agents regarding the agent's role in the emerging strategy of avoidance. This is achieved by picking actions that compromise between energy efficiency and compliance with everyone's inferred avoidance intentions. We evaluate our approach by comparing against a greedy baseline that only maximizes individual efficiency. Simulation results of statistical significance demonstrate that our planner results in a faster uncertainty decrease that facilitates the decision-making process of co-present agents. The algorithm's performance highlights the importance of topological reasoning in decentralized, multi-agent planning and appears promising for real-world applications in crowded human environments.

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