This paper studies the payoff structure of stable cooperation structures in link formation games. Players choose non-cooperatively with whom they want to form a link, and the payoffs are given by the Myerson value of the cooperation structure obtained. We characterize the class of TU-games that ensure the stability of the full cooperation structure, which turns out to be much larger than the class of superadditive TU-games. We then provide an exact characterization of the Moderer and Shapley potential of the link formation game, and establish its equivalence with the potential as defined by Hart and Mas-Colell [Econometrica, 57 (1989), 589--614]. We use this result to show that stable but Pareto dominated graphs can emerge under simple best-response dynamics.