We show how to bound the effect of belief-dependent preferences on choices in sequential two-player games without information about the (higher-order) beliefs of players. The approach can be applied to a class of belief-dependent preferences which includes reciprocity (Dufwenberg and Kirchsteiger, 2004) and guilt aversion (Battigalli and Dufwenberg, 2007) as special cases. We show how the size of the bounds can be substantially reduced by exploiting a specific invariance property common to preferences in this class. We illustrate our approach by analyzing data from a large scale experiment conducted with a sample of participants randomly drawn from the Dutch population. We find that behavior of players in the experiment is consistent with significant guilt aversion: some groups of the population are willing to pay at least 0.16e to avoid 'letting down' another player by 1e. We also find that our approach produces narrow and thus very informative bounds on the effect of reciprocity in the games we consider. Our bounds suggest the model of reciprocity we consider is not a significant determinant of decisions in our experiment.