Repeated social coordination is a crucial aspect of daily life in which individuals strategically distribute labor and resources, often to accomplish complex tasks and goals. However, social coordination is also very challenging because humans often have competing interests, especially when successful coordination persistently leaves one party better off, entrenching inequality. Here we use a novel task, the Asymmetric Social Exchange (ASE) Game, to study how individuals learn to coordinate with different kinds of social partners and how individual trait variability on key social dimensions related to negative evaluation (i.e., social anxiety), impacts compliance with disadvantageous conventions (N = 675). Using two kinds of Bayesian models, one that learns from experience and one that builds a causal model of others' hidden motivations, we show that differences in coordination strategies arise from both individual learning differences and from expressed social preferences. Further, we find that social anxiety increases compliance with disadvantageous payoffs.