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Social distancing, gathering, search games : mobile agents on simple networks
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Alpern, Steve and Zeng, Li (2022) Social distancing, gathering, search games : mobile agents on simple networks. Dynamic Games and Applications, 12 . pp. 288-311. doi:10.1007/s13235-022-00427-1
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Official URL: https://doi.org/10.1007/s13235-022-00427-1
Abstract
During epidemics, the population is asked to socially distance, with pairs of individuals keeping two meters apart. We model this as a new optimization problem by considering a team of agents placed on the nodes of a network. Their common aim is to achieve pairwise graph distances of at least D, a state we call socially distanced. (If D=1, they want to be at distinct nodes; if D=2 they want to be non-adjacent.) We allow only a simple type of motion called a lazy random walk: with probability p (called the laziness parameter), they remain at their current node next period; with complementary probability 1−p, they move to a random adjacent node. The team seeks the common value of p which achieves social distance in the least expected time, which is the absorption time of a Markov chain. We observe that the same Markov chain, with different goals (absorbing states), models the gathering, or multi-rendezvous problem (all agents at the same node). Allowing distinct laziness for two types of agents (searchers and hider) extends the existing literature on predator–prey search games to multiple searchers. We consider only special networks: line, cycle and grid.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Science, Engineering and Medicine > Science > Statistics Faculty of Social Sciences > Warwick Business School |
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| Library of Congress Subject Headings (LCSH): | Search theory, Game theory , Game theory -- Computer programs, Differential games, Epidemics -- Mathematical models, Random walks (Mathematics) | ||||||||
| Journal or Publication Title: | Dynamic Games and Applications | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 2153-0785 | ||||||||
| Official Date: | March 2022 | ||||||||
| Dates: |
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| Volume: | 12 | ||||||||
| Page Range: | pp. 288-311 | ||||||||
| DOI: | 10.1007/s13235-022-00427-1 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s13235-022-00427-1 | ||||||||
| Access rights to Published version: | Open Access | ||||||||
| Description: | Special Issue on Epidemics. This article is part of the topical collection “Modeling and Control of Epidemics” edited by Quanyan Zhu, Elena Gubar and Eitan Altman. |
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