Norms for cooperation are essential for groups to function effectively, yet there are often strong incentives for group members to behave selfishly. Direct and indirect reciprocity can help to discourage such uncooperative behaviour by punishing defectors and rewarding cooperators, but require explicit means for punishment and tally-keeping. What, then, encourages an individual to cooperate with their group when others cannot track the behaviour of others? We adapted the Bargaining Game to examine the emergence and maintenance of cooperation among 20 groups of six anonymous players (N = 120) who interacted amongst themselves over recursive bargaining exchanges. By estimating the expected utility that drives players’ demands in these interactions, we demonstrate that their behaviour on each exchange reflects the demands placed upon them previously. Thus, we highlight the role of generalised reciprocity in such situations; that is, when an individual passes on to another member of their group the behaviour they have received previously. Furthermore, we identify four distinct behavioural types that differ in their expressions of generalised reciprocity: Some players converge quickly on cooperative demands regardless of the behaviour they received from their co-players, and are therefore characterised by low expressions of reciprocity. In contrast, individuals with strong reciprocal tendencies decrease their demands over successive interactions in response to the behaviour of their group. By simulating groups with different compositions of these player types, we reveal the strong influence of individual differences in reciprocal tendencies on the emergence of cooperative group dynamics.