Book excerpt: Mechanism design theories have established basic framework in studying economic problems where agents have private information and behave in their own interests. This framework provides a workhorse for exploring how to implement social choice rules in general. One typical issue is to analyze the decision-making by a social planner or a designer who aims to achieve efficient outcomes that maximize the joint welfare of all agents. Not surprisingly, efficiency essentially requires that the designer know the agents' private information and then choose the corresponding socially optimal outcome. However, the difficulty of mechanism design problem is to characterize these incentive constraints where agents find it optimal to reveal their private information truthfully. Specifically, sufficiently rich private information could entail non-implementability of efficient social choice rules. To overcome this difficulty, this dissertation considers a class of semi-exclusive information structures where agents may observe signals about payoff signals, and a class of problems where agents may have wrong beliefs or the mechanism designer is not informed about the agents' valuation functions, and proposes mechanisms that implement efficient allocations.