[eng] We use a large public dataset of proposer-responder games to examine other-regarding preferences and beliefs. We model preferences and beliefs within a quantal response equi- librium framework using a non-linear mixed logit model that takes individual heterogene- ity into account. Several measures indicate that parameters are reliably identified. Our par- ticipants are heterogeneous with respect to preferences and more so with regard to beliefs about others' preferences. On average, proposers overestimate responders' aversion to ad- vantageous inequality, and think of responders as more averse to advantageous inequality and less averse to disadvantageous inequality than themselves. These findings are consis- tent with an optimism bias.