Nash Welfare and Facility Location

We consider the problem of locating a facility to serve a set of agents located along a line. The Nash welfare objective function, defined as the product of the agents' utilities, is known to provide a compromise between fairness and efficiency in resource allocation problems. We apply this welfare notion to the facility location problem, converting individual costs to utilities and analyzing the facility placement that maximizes the Nash welfare. We give a polynomial-time approximation algorithm to compute this facility location, and prove results suggesting that it achieves a good balance of fairness and efficiency. Finally, we take a mechanism design perspective and propose a strategy-proof mechanism with a bounded approximation ratio for Nash welfare

Reification of network resource control in multi-agent systems

In multi-agent systems [1], coordinated resource sharing is indispensable for a set of autonomous agents, which are running in the same execution space, to accomplish their computational objectives. This research presents a new approach to network resource control in multi-agent systems, based on the CyberOrgs [2] model. This approach aims to offer a mechanism to reify network resource control in multi-agent systems and to realize this mechanism in a prototype system. In order to achieve these objectives, a uniform abstraction vLink (Virtual Link) is introduced to represent network resource, and based on this abstraction, a coherent mechanism of vLink creation, allocation and consumption is developed. This mechanism is enforced in the network by applying a fine-grained flow-based scheduling scheme. In addition, concerns of computations are separated from those of resources required to complete them, which simplifies engineering of network resource control. Thus, application programmers are enabled to focus on their application development and separately declaring resource request and defining resource control policies for their applications in a simplified way. Furthermore, network resource is bounded to computations and controlled in a hierarchy to coordinate network resource usage. A computation and its sub-computations are not allowed to consume resources beyond their resource boundary. However, resources can be traded between different boundaries. In this thesis, the design and implementation of a prototype system is described as well. The prototype system is a middleware system architecture, which can be used to build systems supporting network resource control. This architecture has a layered structure and aims to achieve three goals: (1) providing an interface for programmers to express resource requests for applications and define their resource control policies; (2) specializing the CyberOrgs model to control network resource; and (3) providing carefully designed mechanisms for routing, link sharing and packet scheduling to enforce required resource allocation in the network

Utility Design for Distributed Resource Allocation -- Part I: Characterizing and Optimizing the Exact Price of Anarchy

Game theory has emerged as a fruitful paradigm for the design of networked multiagent systems. A fundamental component of this approach is the design of agents' utility functions so that their self-interested maximization results in a desirable collective behavior. In this work we focus on a well-studied class of distributed resource allocation problems where each agent is requested to select a subset of resources with the goal of optimizing a given system-level objective. Our core contribution is the development of a novel framework to tightly characterize the worst case performance of any resulting Nash equilibrium (price of anarchy) as a function of the chosen agents' utility functions. Leveraging this result, we identify how to design such utilities so as to optimize the price of anarchy through a tractable linear program. This provides us with a priori performance certificates applicable to any existing learning algorithm capable of driving the system to an equilibrium. Part II of this work specializes these results to submodular and supermodular objectives, discusses the complexity of computing Nash equilibria, and provides multiple illustrations of the theoretical findings.Comment: 15 pages, 5 figure

Quantized VCG Mechanisms for Polymatroid Environments

Many network resource allocation problems can be viewed as allocating a divisible resource, where the allocations are constrained to lie in a polymatroid. We consider market-based mechanisms for such problems. Though the Vickrey-Clarke-Groves (VCG) mechanism can provide the efficient allocation with strong incentive properties (namely dominant strategy incentive compatibility), its well-known high communication requirements can prevent it from being used. There have been a number of approaches for reducing the communication costs of VCG by weakening its incentive properties. Here, instead we take a different approach of reducing communication costs via quantization while maintaining VCG's dominant strategy incentive properties. The cost for this approach is a loss in efficiency which we characterize. We first consider quantizing the resource allocations so that agents need only submit a finite number of bids instead of full utility function. We subsequently consider quantizing the agent's bids