This work addresses multi-robot coordination in social human-populated environments using a market-based framework for solving the Multi-Robot Task Allocation (MRTA) problem. Humans are considered in the proposed coordination mechanism by means of accounting for social costs in bid evaluations and requesting collaboration in socially blocking situations. Initially, the effect of a realistic environment with varying number of static/moving humans on the behavior and performance of our method is studied through an extensive suite of experiments in a high-fidelity simulator. Results show that the total traveled distance and time are increased when humans are present in the environments. Localization noise is also increased particularly in the case of static people. In the second series of experiments, a number of problematic cases resulting in longer modified paths, blocked passages, and long waits have been investigated. A comparative study targeting human-agnostic navigation and planning, human-aware navigation and human-agnostic planning, and human-aware navigation and planning has been conducted. Both simulated and real robot experiments confirm the effectiveness of accounting for humans at both team and individual levels. This leads to respecting social constraints as well as achieving a better performance based on MRTA metrics.