Large scale multiagent systems must rely on distributed decision making, as centralized coordination is either impractical or impossible. Recent works approach this problem under a game theoretic lens, whereby utility functions are assigned to each of the agents with the hope that their local optimization approximates the centralized optimal solution. Yet, formal guarantees on the resulting performance cannot be obtained for broad classes of problems without compromising on their accuracy. In this work, we address this concern relative to the well-studied problem of resource allocation with nondecreasing concave welfare functions. We show that optimally designed local utilities achieve an approximation ratio (price of anarchy) of 1-c/e, where c is the function's curvature and e is Euler's constant. The upshot of our contributions is the design of approximation algorithms that are distributed and efficient, and whose performance matches that of the best existing polynomial-time (and centralized) schemes.

翻译：大型多试剂系统必须依靠分布式决策,因为集中协调要么不切实际,要么不可能。最近的工程在游戏理论角度下处理这一问题,即将公用事业功能分配给每个代理商,希望它们的地方优化接近集中式最佳解决办法。然而,无法在不损害其准确性的情况下对由此产生的一系列问题获得正式的履约保证。在这项工作中,我们解决了人们深思熟虑的资源分配问题,即与未缩减的混凝土福利功能有关的资源分配问题。我们表明,设计最优化的本地公用事业实现了1-c/e的近似率(无政府状态价格),c是功能的曲线,e是Euler的常数。我们贡献的亮点是分布和高效的近似算算法设计,其性能与现有最佳的多元(和集中)时间(和)计划相匹配。