Data-driven predictions are often perceived as inaccurate in hindsight due to behavioral responses. In this study, we explore the role of interface design choices in shaping individuals' decision-making processes in response to predictions presented on a shared information display in a strategic setting. We introduce a novel staged experimental design to investigate the effects of design features, such as visualizations of prediction uncertainty and error, within a repeated congestion game. In this game, participants assume the role of taxi drivers and use a shared information display to decide where to search for their next ride. Our experimental design endows agents with varying level-$k$ depths of thinking, allowing some agents to possess greater sophistication in anticipating the decisions of others using the same information display. Through several extensive experiments, we identify trade-offs between displays that optimize individual decisions and those that best serve the collective social welfare of the system. We find that the influence of display characteristics varies based on an agent's strategic sophistication. We observe that design choices promoting individual-level decision-making can lead to suboptimal system outcomes, as manifested by a lower realization of potential social welfare. However, this decline in social welfare is offset by a reduction in the distribution shift, narrowing the gap between predicted and realized system outcomes, which potentially enhances the perceived reliability and trustworthiness of the information display post hoc. Our findings pave the way for new research questions concerning the design of effective prediction interfaces in strategic environments.