This paper presents a GA-based multi-agent reinforcement learning bidding approach (GMARLB) for performing multi-agent reinforcement learning. GMARLB integrates reinforcement learning, bidding and genetic algorithms. The general idea of our multi-agent systems is as follows: There are a number of individual agents in a team, each agent of the team has two modules: Q module and CQ module. Each agent can select actions to be performed at each step, which are done by the Q module. While the CQ module determines at each step whether the agent should continue or relinquish control. Once an agent relinquishes its control, a new agent is selected by bidding algorithms. We applied GA-based GMARLB to the Backgammon game. The experimental results show GMARLB can achieve a superior level of performance in game-playing, outperforming PubEval, while the system uses zero built-in knowledge.