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Multi-agent interactions are important to model for forecasting other agents' behaviors and trajectories. At a certain time, to forecast a reasonable future trajectory, each agent needs to pay attention to the interactions with only a small group of most relevant agents instead of unnecessarily paying attention to all the other agents. However, existing attention modeling works ignore that human attention in driving does not change rapidly, and may introduce fluctuating attention across time steps. In this paper, we formulate an attention model for multi-agent interactions based on a total variation temporal smoothness prior and propose a trajectory prediction architecture that leverages the knowledge of these attended interactions. We demonstrate how the total variation attention prior along with the new sequence prediction loss terms leads to smoother attention and more sample-efficient learning of multi-agent trajectory prediction, and show its advantages in terms of prediction accuracy by comparing it with the state-of-the-art approaches on both synthetic and naturalistic driving data. We demonstrate the performance of our algorithm for trajectory prediction on the INTERACTION dataset on our website.