A popular fundraising tool is donation matching, where every dollar is matched by a third party. But field experiments find that matching does not always increase donations. This may occur because individuals believe that peer donors will exhaust the matching funds, so their donation is not pivotal to obtaining matching funds. We develop a theory of how beliefs about peers' donations affect one's own likelihood of donation. We test our theory using novel "threshold match" treatments in field and laboratory experiments. These treatments form small groups and offer a flat matching bonus if a threshold number of donations is received. One "threshold match" treatment more than doubles the donation rate in the field relative to no match. To better understand the mechanism behind this huge increase, we use a lab study to replicate the field results and further show that beliefs about peers' donations matter. Our theoretical, lab, and field results combined suggest people are more likely to donate when they believe they are more pivotal to securing matching money. Beliefs about others matter, and they should be taken into account when trying to increase donations.