Mechanism design is studied for aggregating renewable power producers (RPPs) in a two-settlement power market. Employing an indirect mechanism design framework, a payoff allocation mechanism (PAM) is derived from the competitive equilibrium (CE) of a specially formulated market with transferrable payoff. Given the designed mechanism, the strategic behaviors of the participating RPPs entail a non-cooperative game: It is proven that a unique pure Nash equilibrium (NE) exists among the RPPs, for which a closed-form expression is found. Moreover, it is proven that the designed mechanism achieves a number of key desirable properties at the NE: these include efficiency (i.e., an ideal "Price of Anarchy" of one), stability (i.e., "in the core" from a coalitional game theoretic perspective), and no collusion. In addition, it is shown that a set of desirable "ex-post" properties are also achieved by the designed mechanism. Extensive simulations are conducted and corroborate the theoretical results.