线性约束下社会效用最大化的一般机制设计方法
A General Mechanism Design Methodology for Social Utility Maximization with Linear Constraints
摘要：
社会效用最大化是指在系统约束条件下，使各主体的效用之和最大化的资源配置过程。这种分配在包括单播的一般通信领域中的几个问题中出现（和多播多速率）服务，以及在具有（本地）公共产品的应用中，例如无线网络中的功率分配、频谱分配等。还研究了在纳什均衡中实现这种分配的机制，但是它们要么不具有完全的实现属性，或者以个案的方式给出，从而模糊了对这些问题的基本理解。在本文中，我们提出了一个统一的方法来创建机制，充分实现，在纳什均衡，社会效用最大化的功能，在各种情况下，约束是凸的。通过考虑对偶优化问题，以系统的方式进行机制的构建。除了这种机制应该满足的效率和个人理性的必要属性之外，本文还重点讨论了三个额外的设计目标：a）消息空间的大小随代理的数量线性缩放（即使代理人的类型是整个价值函数），b）分配是可行的，在和非均衡，（3）在需求可行时，在均衡和非均衡时都有强劲的预算平衡。
英文摘要：
Social utility maximization refers to the process of allocating resources in such a way that the sum of agents' utilities is maximized under the system constraints. Such allocation arises in several problems in the general area of communications, including unicast (and multicast multi-rate) service on the Internet, as well as in applications with (local) public goods, such as power allocation in wireless networks, spectrum allocation, etc. Mechanisms that implement such allocations in Nash equilibrium have also been studied but either they do not possess full implementation property, or are given in a case-by-case fashion, thus obscuring fundamental understanding of these problems. In this paper we propose a unified methodology for creating mechanisms that fully implement, in Nash equilibria, social utility maximizing functions arising in various contexts where the constraints are convex. The construction of the mechanism is done in a systematic way by considering the dual optimization problem. In addition to the required properties of efficiency and individual rationality that such mechanisms ought to satisfy, three additional design goals are the focus of this paper: a) the size of the message space scaling linearly with the number of agents (even if agents' types are entire valuation functions), b) allocation being feasible on and off equilibrium, and c) strong budget balance at equilibrium and also off equilibrium whenever demand is feasible.
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