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Information theoretic cutting of a cake
, Article IEEE Transactions on Information Theory ; Volume 63, Issue 11 , 2017 , Pages 6950-6978 ; 00189448 (ISSN) ; Gohari, A ; Sharif University of Technology
Abstract
Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e., one agent may like chocolate, while the other may like cream). A fair division of the cake is one that takes into account the individual valuations of agents and partitions of the cake based on some fairness criterion. Fair division may be accomplished in a distributed or centralized way. Due to its natural and practical appeal, it has been a subject of study in economics. To the best of our knowledge, the role of partial information in fair division has not been studied so far from an...
Envy-free mechanisms with minimum number of cuts
, Article 31st AAAI Conference on Artificial Intelligence, AAAI 2017, 4 February 2017 through 10 February 2017 ; 2017 , Pages 312-318 ; Farhadi, M ; Ghodsi, M ; Seddighin, M ; Tajik, A. S ; Amazon; Artificial Intelligence; Baidu; et al.; IBM; Tencent ; Sharif University of Technology
AAAI press
2017
Abstract
We study the problem of fair division of a heterogeneous resource among strategic players. Given a divisible heterogeneous cake, we wish to divide the cake among n players in a way that meets the following criteria: (I) every player (weakly) prefers his allocated cake to any other player's share (such notion is known as envy-freeness), (II) the mechanism is strategy-proof (truthful), and (III) the number of cuts made on the cake is minimal. We provide methods, namely expansion process and expansion process with unlocking, for dividing the cake under different assumptions on the valuation functions of the players. Copyright © 2017, Association for the Advancement of Artificial Intelligence...
Fair and Strategic Division of Resources
, Ph.D. Dissertation Sharif University of Technology ; Ghodsi, Mohammad (Supervisor)
Abstract
In this study, we consider the fair division problem. In this problem, a heterogeneous resource must be fairly divided among a set of agents with different preferences.The resource can be either a divisible good (i.e., time, land), or a set of indivisible goods. When the resource is a single divisible good, the problem is commonly known as cake cutting. To measure fairness, several notions are defined, i.e., envy-freeness, proportionality, equability, maximin-share. In this thesis, we first give a formal definition of these notions. Next, we present our results for envy-freeness and maximin-share.First, we prove the existence of an allocation that guarantees each agent a factor 3/4 of his...