On the nonexistence of stationary solutions in bio-inspired collective decision making via mean-field game
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.Citation
Stella, L. and Bauso, D., (2017). 'On the nonexistence of stationary solutions in bio-inspired collective decision making via mean-field game'. IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, VIC, Australia, 12-15 Dec. New York: IEEE, pp. 787-792.Publisher
IEEEJournal
2017 IEEE 56th Annual Conference on Decision and Control (CDC)DOI
10.1109/cdc.2017.8263756Type
Meetings and ProceedingsLanguage
enISSN
9781509028733ae974a485f413a2113503eed53cd6c53
10.1109/cdc.2017.8263756