The existence of generalized exchange characterized by unilateral resource giving has been a puzzle when we assume rational actors, because free riding can occur. This article first identifies pure-generalized exchange in which each actor gives resources to the recipient(s) of his choice. Then, it proposes the fairness-based selective-giving strategy. An actor adopting this strategy selects a recipient whose behaviors satisfy her criterion of fairness, provided perfect information is given. The results of evolutionary simulation show that pure-generalized exchange can emerge among egoists without collective norms, even in societies in which individuals have information only about their immediate neighbors.