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Some group activities, such as team sports and choreographed dances, involve closely coupled interaction between participants. Here we investigate the tasks of inferring and predicting participant behavior, in terms of motion paths and actions, under such conditions. We narrow the problem to that of estimating how a set target participants react to the behavior of other observed participants. Our key idea is to model the spatio-temporal relations among participants in a manner that is robust to error accumulation during frame-wise inference and prediction. We propose a novel Entry-Flipped Transformer (EF-Transformer), which models the relations of participants by attention mechanisms on both spatial and temporal domains. Unlike typical transformers, we tackle the problem of error accumulation by flipping the order of query, key, and value entries, to increase the importance and fidelity of observed features in the current frame. Comparative experiments show that our EF-Transformer achieves the best performance on a newly-collected tennis doubles dataset, a Ceilidh dance dataset, and two pedestrian datasets. Furthermore, it is also demonstrated that our EF-Transformer is better at limiting accumulated errors and recovering from wrong estimations.