Fair and Efficient Resource Allocation

Abstract

We address the problem of achieving fair and efficient allocation of resources in the era of rapid technological advancements, including Artificial Intelligence (AI) and the Internet of Things (IoT). The allocation of resources among autonomous agents is a crucial problem, and achieving fairness while ensuring efficiency is challenging. The objective is to determine the best way to divide resources among interested agents so that everyone is happy with their allocation, while ensuring fairness. We explore various fairness notions and relaxations that could apply to the problem of resource allocation. One of the main issues addressed in the thesis is the challenge of achieving fairness in the allocation of indivisible resources. We address several critical questions related to fair division, such as how to ensure fairness, how to generalize the notion of fairness, and what criteria to choose for different contexts. On top of it, fair division for goods and chores requires different approaches. We examine this issue in more detail and survey the existing approaches and provide solutions to overcome the challenges. We provide a detail survey on fairness notion and their approximate relaxations and evaluates their effectiveness in achieving fair and efficient allocations. In recent literature, researchers have delved into data-driven approaches in game theory and mechanism design to tackle the challenges of traditional approaches. Given the success of neural networks (NNs) in learning algorithms, and mechanisms, and solving mixedinteger programs, they offer a promising tool for achieving fair and efficient allocations of resources. Thus, we aim to use NNs to find an approximate fair allocation that maximizes social welfare in our pursuit of equitable and efficient resource distribution. Another criticaL issue addressed in the thesis is the presence of externalities, where the utility of an agent depends not only on their allocated resources but also on the resources allocated to other agents. Such scenarios are prevalent, especially in allocating critical resources such as hospital beds, ventilators, and vaccines during the COVID-19 pandemic. We evaluate the challenges of achieving fair and efficient allocations in the presence of externalities and propose potential solutions. Overall, in this thesis, we provide a comprehensive analysis of the challenges of achieving fair and efficient allocation of resources in the era of rapid technological advancements. The research proposes efficient algorithms and solutions to overcome the challenges and achieve approximately fair allocation in different contexts. Achieving fair and efficient resource allocation is crucial for various domains, including economics, politics, and social welfare, and the results of this could have significant implications in these domains.