Reciprocal altruism has been the backbone of research on the evolution of altruistic behaviour towards non-kin, but recent research has begun to apply costly signalling theory to this problem. In addition to signaling resources or abilities, public generosity could function as a costly signal of cooperative intent, benefiting altruists in terms of (i) better access to cooperative relationships and (ii) greater cooperation within those relationships. When future interaction partners can choose with whom they wish to interact, this could lead to competition to be more generous than others. Little empirical work has tested for the possible existence of this ‘competitive altruism’. Using a cooperative monetary game with and without opportunities for partner choice and signalling cooperative intent, we show here that people actively compete to be more generous than others when they can benefit from being chosen for cooperative partnerships, and the most generous people are correspondingly chosen more often as cooperative partners. We also found evidence for increased scepticism of altruistic signals when the potential reputational benefits for dishonest signalling were high. Thus, this work supports the hypothesis that public generosity can be a signal of cooperative intent, which people sometimes ‘fake’ when conditions permit it.