离散多项分布与匿名对策中的Nash均衡
Discretized Multinomial Distributions and Nash Equilibria in Anonymous Games
摘要：
我们发现，有一个多项式时间近似计划计算纳什均衡匿名游戏的任何固定数量的战略（一类非常广泛和重要的游戏），扩展Daskalakis和Papadimitriou 2007年的两个战略的结果。近似保证来自更普遍感兴趣的概率结果：具有范围在{e1，e2，.，ek}，其中ei是沿着k维欧几里德空间的维度i的单位向量，可以通过另一组独立单位向量的和的分布来近似，对于某个整数z，获得每个值的概率是1/z的倍数，并且使得两个分布的变分距离至多为eps，其中eps由z中的逆多项式和k的函数限定，但不依赖于n。我们的概率结果指定建设一个令人惊讶的稀疏eps覆盖-下的总变化距离-的一组分布的总和独立的单位向量，这是感兴趣的权利。
英文摘要：
We show that there is a polynomial-time approximation scheme for computing Nash equilibria in anonymous games with any fixed number of strategies (a very broad and important class of games), extending the two-strategy result of Daskalakis and Papadimitriou 2007. The approximation guarantee follows from a probabilistic result of more general interest: The distribution of the sum of n independent unit vectors with values ranging over {e1, e2, ...,ek}, where ei is the unit vector along dimension i of the k-dimensional Euclidean space, can be approximated by the distribution of the sum of another set of independent unit vectors whose probabilities of obtaining each value are multiples of 1/z for some integer z, and so that the variational distance of the two distributions is at most eps, where eps is bounded by an inverse polynomial in z and a function of k, but with no dependence on n. Our probabilistic result specifies the construction of a surprisingly sparse eps-cover -- under the total variation distance -- of the set of distributions of sums of independent unit vectors, which is of interest on its own right.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
