Affiliation:
1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560012, India;
2. Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Abstract
This work develops algorithmic results for the classic cake-cutting problem in which a divisible, heterogeneous resource (modeled as a cake) needs to be partitioned among agents with distinct preferences. We focus on a standard formulation of cake cutting wherein each agent must receive a contiguous piece of the cake. Although multiple hardness results exist in this setup for finding fair/efficient cake divisions, we show that, if the value densities of the agents satisfy the monotone likelihood ratio property (MLRP), then strong algorithmic results hold for various notions of fairness and economic efficiency. Addressing cake-cutting instances with MLRP, first we develop an algorithm that finds cake divisions (with connected pieces) that are envy free, up to an arbitrary precision. The time complexity of our algorithm is polynomial in the number of agents and the bit complexity of an underlying Lipschitz constant. We obtain similar positive results for maximizing social, egalitarian, and Nash social welfare. Many distribution families bear MLRP. In particular, this property holds if all the value densities belong to any one of the following families: Gaussian (with the same variance), linear, Poisson, and exponential distributions, linear translations of any log-concave function. Hence, through MLRP, the current work obtains novel cake-cutting algorithms for multiple distribution families.
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Subject
Management Science and Operations Research,Computer Science Applications,General Mathematics
Cited by
2 articles.
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1. A Discrete and Bounded Locally Envy-Free Cake Cutting Protocol on Trees;Web and Internet Economics;2023-12-31
2. Envy-Free Cake-Cutting for Four Agents;2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS);2023-11-06