This paper studies distributed multi-relay selection in energy-harvesting cooperative wireless networks and models it as an Indian Buffet Game (IBG). Particularly, the IBG is utilized to model the multirelay selection decisions of network source nodes, while account for negative network externality. Two scenarios are considered: (1) constrained selections (CS), and (2) unconstrained selections (US). In the former scenario, each source is constrained to a maximum number of relay selections; while in the latter scenario, the source nodes can select as many relays as possible. Since the relays are energy-harvesting-and thus intermittently harvest random amounts of energy-the accumulated energy at each relay is unknown to the source nodes, leading to uncertain relays' energy states. In turn, a non-Bayesian learning (NBL) algorithm is devised for the source nodes to learn the relays' energy states. After that, two distributed best-response (BR) recursive algorithms, namely BR-CS and BR-US, are proposed to allow the source nodes to make multi-relay selection decisions, while guaranteeing subgame perfect Nash equilib-This work is partially supported by the Kuwait Foundation for the Advancement of Sciences (KFAS), under project code PN17-15EE-02.