We consider the question of implementability of a social choice function in a classical setting where the preferences of finitely many selfish individuals with private information have to be aggregated towards a social choice. This is one of the central questions in mechanism design. If the concept of weak implementation is considered, the Revelation Principle states that one can restrict attention to truthful implementations and direct revelation mechanisms, which implies that implementability of a social choice function is easy to check. For the concept of strong implementation, however, the Revelation Principle becomes invalid, and the complexity of deciding whether a given social choice function is strongly implementable has been open so far. In this paper, we show by using methods from polyhedral theory that strong implementability of a social choice function can be decided in polynomial space and that each of the payments needed for strong implementation can always be chosen to be of polynomial encoding length. Moreover, we show that strong implementability of a social choice function involving only a single selfish individual can be decided in polynomial time via linear programming.
A strong direct product theorem for two-way public coin communication complexity
根据我们定义的新复杂性度量，我们展示了所有关系的双向公共币通信复杂性的直接结果。我们的新测度是[J，Klauck and Nayak 08]中的双向乘积子分布界对非乘积分布的推广，从而我们的结果隐含了它们在双向乘积子分布界方面的直接乘积结果.我们证明了我们新的复杂性度量给出了集合不相交问题的紧下界，因此我们重现了这个问题的强直积结果，这是以前由[Klauck 00]证明的。
Strong direct product conjecture holds for all relations in public coin randomized one-way communication complexity
设X x Y x Z的f子集是一个关系.让f的公共硬币单向通信复杂性，最坏情况误差为1/3，表示为R^{1，pub}_{1/3}（f）。我们证明了如果对于计算f^k（k个f的独立副本），提供o（k R^{1，pub}_{1/3}（f））通信，则成功在k中是指数小的。这解决了公共硬币单向通信复杂性中所有关系的强直积猜想。我们展示了公共硬币单向通信复杂性的新的紧密表征，其加强了[J.，Klauck，Nayak 08].我们使用新的表征，以显示我们的直接产品的结果，这也可能是独立的利益。
