We present a novel algorithm for game-theoretic trajectory planning, tailored for settings in which agents can only observe one another in specific regions of the state space. Such problems arise naturally in the context of multi-robot navigation, where occlusions due to environment geometry naturally mask agents' view of one another. In this paper, we formalize these settings as dynamic games with a hybrid information structure, which interleaves so-called "open-loop" periods (in which agents cannot observe one another) with "feedback" periods (with full state observability). We present two main contributions. First, we study a canonical variant of these hybrid information games in which agents' dynamics are linear, and objectives are convex and quadratic. Here, we build upon classical solution methods for the open-loop and feedback variants of these games to derive an algorithm for the hybrid information case that matches the cubic runtime of the classical settings. Second, we consider a far broader class of problems in which agents' dynamics are nonlinear, and objectives are nonquadratic; we reduce these problems to sequences of hybrid information linear-quadratic games and empirically demonstrate that iteratively solving these simpler problems with the proposed algorithm yields reliable convergence to approximate Nash equilibria through simulation studies of overtaking and intersection traffic scenarios.
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