Abstract: To cooperate or compete rationally in continuous, partially observable multi-agent spaces, game theoretic agents must make plans that optimally gather information about their opponents. These problems are modeled by partially observable stochastic games (POSGs), but planning in fully continuous POSGs is intractable without heavy offline computation or assumptions on the order of belief players maintain. We formulate a finite history/horizon refinement of POSGs which admits competitive information gathering behavior in trajectory space, and through a series of approximations, we present an online method for computing rational trajectory plans in these games, leveraging particle-based estimations of the joint state space to perform stochastic gradient play. We also provide the necessary adjustments required to deploy this method on individual agents. The method is tested in continuous pursuit-evasion and warehouse-pickup scenarios (alongside extensions to N>2 players and to more complex environments with visual and physical obstacles), demonstrating evidence of active information gathering and outperforming passive competitors.