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Maximin share guarantee for goods with positive externalities

Seddighin, M ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1007/s00355-020-01278-8
  3. Publisher: Springer , 2020
  4. Abstract:
  5. One of the important yet insufficiently studied subjects in fair allocation is the externality effect among agents. For a resource allocation problem, externalities imply that the share allocated to an agent may affect the utilities of other agents. In this paper, we conduct a study of fair allocation of indivisible goods with positive externalities. Inspired by the models in the context of network diffusion, we present a simple and natural model, namely network externalities, to capture the externalities. To evaluate fairness in the network externalities model, we generalize the idea behind the notion of maximin-share (MMS) to achieve a new criterion, namely, extended-maximin-share (EMMS). Next, we consider two problems concerning our model. First, we discuss the computational aspects of finding the value of EMMS for every agent. For this, we introduce a generalized form of partitioning problem that includes many famous partitioning problems such as maximin, minimax, and leximin. We further show that a 1/2-approximation algorithm exists for this partitioning problem. Next, we investigate approximate EMMS allocations, i.e., allocations that guarantee each agent a utility of at least a fraction of his extended-maximin-share. We show that under a natural assumption that the agents are α-self-reliant, an α/ 2 -EMMS allocation always exists. This, combined with the former result yields a polynomial-time α/ 4 -EMMS allocation algorithm. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature
  6. Keywords:
  8. Source: Social Choice and Welfare ; 2020
  9. URL: https://link.springer.com/article/10.1007/s00355-020-01278-8