Empiricists often struggle to apply game theory models to real-life cases of animal cooperation. One reason is that many examples of cooperation occur in stable groups, where individuals form social bonds that influence exchanges of help in ways that are not well described by previous models, including the extent of reciprocity and how relationships are initiated. We present a game theory model exploring the conditions under which social bonds between group members promote cooperation. In the model, bonds build up from exchanges of help in a similar way as the strength of association increases in learning, as in the Rescorla–Wagner rule. The bonds in turn affect partner choice and influence helping amounts. The model has a mechanism of reciprocity for bonded pairs, which can evolve toward either loose or strict reciprocation. Several aspects of the model are inspired by observations of food sharing in vampire bats. We find that small social neighborhoods are required for the evolutionary stability of helping, either as small group sizes, or if bonded members of larger groups can form temporary (daily) smaller groupings. The costs of helping need to be fairly low, while the benefits can be substantial. The form of reciprocity that evolves is neither immediate nor very strict. Individuals in need request help based on bond strength, but there is also an evolved preference for initiating bonds with new group members. In contrast, if different groups come into temporary contact, the evolved tendency is to avoid forming bonds between groups.