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.
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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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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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