On the nonexistence of stationary solutions in bio-inspired collective decision making via mean-field game

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Stella, Leonardo and Bauso, Dario 2017. On the nonexistence of stationary solutions in bio-inspired collective decision making via mean-field game. IEEE. https://doi.org/10.1109/cdc.2017.8263756
AuthorsStella, Leonardo and Bauso, Dario
Abstract

Conditions for nonexistence of stationary solutions in collective decision making are investigated via discrete-state continuous-time mean-field games. The study builds on a bio-inspired model in honeybee swarms. The ultimate goal is to find the best alternative decision in a collective fashion. A cross-inhibition signal, as the one observed in honeybee swarms, is used to capture different types of failures, including disrupted communication channels, computational errors or malevolent behaviour. The model is based on the hypotheses that players control their transition rates from one state to another to minimise a cost, under the presence of an adversarial disturbance. The cost to minimise involves a penalty on control and a congestion-dependent term. As a main result, we prove that the solution obtained as the asymptotic limit of the nonstationary one can be approximated by a closed orbit trajectory. This argument is used to prove the nonexistence of stationary solution under certain conditions.

KeywordsGames, Biological system modeling, Mathematical model, Markov processes, Numerical models, Decision making
Year2017
Journal2017 IEEE 56th Annual Conference on Decision and Control (CDC)
2017 IEEE 56th Annual Conference on Decision and Control (CDC)
PublisherIEEE
ISSN9781509028733
Digital Object Identifier (DOI)https://doi.org/10.1109/cdc.2017.8263756
Web address (URL)http://hdl.handle.net/10545/624660
hdl:10545/624660
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File Access Level
Open
Publication datesDec 2017
Publication process dates
Deposited06 Apr 2020, 09:06
Accepted2017
ContributorsUniversity of Sheffield
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