Fair and Efficient Cake Cutting

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Mirfakhar, Amir Mahdi | 2021

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55252 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Ghodsi, Mohammad
Abstract:
Cake Cutting is an old problem that studies how to allocate a resource among a number of agents to achieve fairness or maximize the revenue by selling the chunks fairly. The primary assumption in the conventional methods of studying Cake Cutting was that the allocator knows everything about the agents and their valuation functions for the different cuts of the cake, which could be impossible in real life. Here we addressed a new setting for an online Cake Cutting problem with unconnected pieces and studied four different objectives upon the setting. There we studied fair and efficient Online Cake Cutting by means of linear fairness and envy freeness. We also added a payment rule to study the revenue-maximizing resource allocation problem. In the last section, we generalized the EF-1 Round-Robin algorithm to achieve envy freeness in an online setting. The central assumption in all sections was to assure that the allocator did not know anything about the agents and their valuation functions. We proposed different algorithms to solve all of the mentioned problems with sub-linear regret functions and meticulously analyzed their efficiency.
Keywords:
Fairness ; Agents ; Approximate Algorithm ; Envy-Free Division ; Revenue Management ; Sub-Linear Regret ; Cake Cutting ; Full Information