The authors examine the stochastic stability of a process of learning and evolution in a gift-giving game. Overlapping generations of players are randomly matched to play the game. The players may consult information systems to learn about the past behavior of their opponents. If the value of the gift is ``smaller than twice'' (resp. ``more than four times'') the cost, then gifts are ``not given'' (resp. ``exchanged''). In the stochastically stable equilibrium, a unique information system is selected to support cooperation.