With increasing flood risk, evacuation has become an important research topic in urban flood management. Urban flood evacuation is a complex problem due to i) the complex interactions among several components within a city and ii) the need to consider multiple, often competing, dimensions/objectives in evacuation analysis. In this study, we focused on the interplay between two such objectives: efficiency and fairness. We captured the evacuation process in a conceptual agent-based model (ABM), which was analyzed under different hard infrastructure and institutional arrangement conditions, namely, various shelter capacity distributions as a hard infrastructure property and simultaneous/staged evacuation as an institutional arrangement. Efficiency was measured as the time it takes for a person to evacuate to safety. Fairness was defined by how equally residents suffered from floods, and the level of suffering depended on the perceived risk and evacuation time. Our findings suggested that efficiency is more sensitive to the shelter capacity distribution, while fairness changes more notably according to the evacuation priority assigned to the divided zones in staged evacuation. Simultaneous evacuation generally tended to be more efficient but unfairer than staged evacuation. The efficiency-fairness trade-off was captured by Pareto-optimal strategies, among which uniform capacity cases led to a higher efficiency while prioritizing high-risk residents increases fairness. Strategies balancing efficiency and fairness featured a uniform capacity and prioritized high-risk residents at an intermediate time delay. These findings more clearly exposed the interactions between different factors and could be adopted as benchmarks to inform more complicated evacuation ABMs.