We conducted ultimatum games in which a proposer offers a division of $10 to a respondent, who accepts or rejects it. If an offer is rejected, players receive a known outside option. Our proposers made simultaneous offers to two respondents, with outside options of $2 and $4. The rate of rejected offers was higher than in similar studies, around 50%, and persisted across five trials. Outside options seem to make players "egocentrically" apply different interpretations of the amount being divided, which creates persistent disagreement. And half of respondents demand more when they know other respondents are being offered more. Journal of Economic Literature Classification Numbers: 026, 215.