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Optimal Resource Allocation over Networks via Lottery-Based Mechanisms

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Game Theory for Networks (GameNets 2019)

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Abstract

We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization problem, called the system problem, to find the optimal lottery allocation. The system problem exhibits a two-layer structure comprised of a permutation profile and optimal allocations given the permutation profile. For any fixed permutation profile, we provide a market-based mechanism to find the optimal allocations and prove the existence of equilibrium prices. We show that the system problem has a duality gap, in general, and that the primal problem is NP-hard. We then consider a relaxation of the system problem and derive some qualitative features of the optimal lottery structure.

Research supported by the NSF Science and Technology Center grant CCF- 0939370: “Science of Information”, the NSF grants ECCS-1343398, CNS-1527846 and CIF-1618145, and the William and Flora Hewlett Foundation supported Center for Long Term Cybersecurity at Berkeley.

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Authors and Affiliations

  1. University of California at Berkeley, Berkeley, CA, 94720, USA

    Soham Phade & Venkat Anantharam

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  1. Soham Phade
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  2. Venkat Anantharam
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Correspondence to Soham Phade .

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Editors and Affiliations

  1. Inria Sophia Antipolis, Sophia Antipolis Cedex, France

    Konstantin Avrachenkov

  2. Tsinghua University, Beijing, China

    Longbo Huang

  3. University of California, Santa Barbara, CA, USA

    Jason R. Marden

  4. Telecom ParisTech (ENST), Paris Cedex, France

    Marceau Coupechoux

  5. Sorbonne Université, Paris Cedex, France

    Anastasios Giovanidis

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© 2019 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Phade, S., Anantharam, V. (2019). Optimal Resource Allocation over Networks via Lottery-Based Mechanisms. In: Avrachenkov, K., Huang, L., Marden, J., Coupechoux, M., Giovanidis, A. (eds) Game Theory for Networks. GameNets 2019. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-030-16989-3_4

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  • DOI: https://doi.org/10.1007/978-3-030-16989-3_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-16988-6

  • Online ISBN: 978-3-030-16989-3

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