Abstract: The new understanding of the mechanism and the concept of incentive compatibility make the mechanism design framework established, the display principle greatly simplifies the analytical framework. The public goods economy is difficult to effectively balance the allocation efficiency, voluntary participation and incentive compatibility. The dominant strategy equilibrium mechanism provided by the public goods can lead to strict Pareto ineffective and authoritarian respectively in the quasi-linear environment and the general economic environment. In Bayesian environment, for both public goods economy and private goods economy, Pareto efficiency and voluntary participation are hardly compatible. Among them, the incompatibility of public goods still holds at the limit angle. The Nash implementation and its expansion try to make all the balanced results in the given mechanisms the optimum for the objectives of social choices. To relax the assumption about the information structure and reason, the latest developments of the theories are unfolded around the endogeny of the information structure, a stable mechanism, and the issues of computing mechanism design.

Key words: social choice rules; incentive compatibility; display principle; implementation theory; computing mechanism design