The question of whether a punishment system or a reward system more effectively promotes cooperation in public goods games is still disputatious in social psychology. We proposed a Generalized Meta-Sanction Game which integrates positive reaction such as reward and negative reaction such as punishment. We categorize the parts of the game using structural conditions and regions of attraction to cooperation. According the simulation and theoretical results, some insights are derived such that one should use the second-level on rewarding if a designer of this game would like to use reward-side effect, another mechanism must be needed for keeping cooperation in a system without reward side, and a meta-reward system is more effective than a meta-punishment system.The question of whether a punishment system or a reward system more effectively promotes cooperation in public goods games is still disputatious in social psychology. We proposed a Generalized Meta-Sanction Game which integrates positive reaction such as reward and negative reaction such as punishment. We categorize the parts of the game using structural conditions and regions of attraction to cooperation. According the simulation and theoretical results, some insights are derived such that one should use the second-level on rewarding if a designer of this game would like to use reward-side effect, another mechanism must be needed for keeping cooperation in a system without reward side, and a meta-reward system is more effective than a meta-punishment system.