Public good games are a metaphor for modeling cooperative behavior in groups in the presence of incentives to free ride. In the model presented here agents play a public good game with their neighbors in a social network structure. Agents' decision rules in our model are inspired by elementary learning observed in laboratory and online behavioral experiments involving human participants with the same amount of information, i.e., when individuals only know their own current contribution and their own cumulated payoff. In addition, agents in the model are allowed to severe links with groups in which their payoff is lower and create links to a new randomly chosen group. Reinforcing the results obtained in network scenarios where agents play Prisoner's Dilemma games, we show that thanks to this relinking possibility, the whole system reaches higher levels of average contribution with respect to the case in which the network cannot change. Our setup opens new frameworks to be investigated, and potentially confirmed, through controlled human experiments.