On the tradeoff among efficiency, fairness and revenue in resource allocation

• Main Author: Hua, Xia
• Other Authors: Chen Ning
• Format: Theses and Dissertations
• Language: English
• Published: 2012
• Subjects: DRNTU::Science::Mathematics::Discrete mathematics::Algorithms
• Online Access: https://hdl.handle.net/10356/50746
• Institution: Nanyang Technological University

Resource allocation is a fundamental problem studied extensively in economics, social sciences and computer science, due to its vast applications. Our focus is to consider different solution concepts that capture different perspectives in the market. These solution concepts generally have three factors: fairness from the consumers' perspective, efficiency from the centralized authority's global point of view, and revenue from the market maker's perspective (if we take payment into consideration). In the thesis we will consider a number of problems raised in the market and try to capture fairness, efficiency and revenue in different circumstances. First, in the centralized combinatorial market, taking market maker's perspective into consideration, we study a solution concept called Envy-free Pareto-efficient pricing that strikes a balance among all the three factors. It captures fairness and balances the tradeoff between efficiency and revenue. Specifically, we consider Envy-free Pareto-efficient pricing in two domains, unit demand and single-minded consumers, and analyze its existence, computation, and economic properties. Secondly, we address the following question to capture the tradeoff relation between fairness and efficiency: For any given constants rf and rw, does there exist an allocation that simultaneously achieves fairness approximation ratio rf and welfare approximation ratio rw? We considered two classic resource allocation models under this question: the indivisible-item allocation with subadditive functions and the multiple fractional knapsack allocation with capacities and demands. For both models, we give (nearly) optimal constant bounds on fairness and welfare bifactor approximations regardless of computational constraints. Furthermore, in the cake cutting model, we study the computational complexity of computing an efficiency optimal division given that the allocation satisfies proportional fairness and assigns each agent a connected piece. For linear valuation functions, we provide a polynomial time approximation scheme to compute an efficiency optimal allocation. On the other hand, we show that the problem is NP-hard to approximate within a factor of for general piecewise constant valuation functions.