We develop an evolutionary method that combines reinforcement learning and fictitious playing to seek equilibrium solution for a multi-agent and multi-stage game in the context of supply chain procurement. The game is designed to model task delegation among a group of self-interested transportation companies which serve logistic shipment. The game involves more than two agents and multiple stages of matrix games. The integration of reinforcement learning and fictitious play overcomes the weaknesses of each approach and exploits their strengths. This innovative approach performs extraordinarily well on a game with three players, unknown number of stages, and large gaps of payoff values.