Passivity analysis of higher order evolutionary dynamics and population games

Handle URI:
http://hdl.handle.net/10754/622792
Title:
Passivity analysis of higher order evolutionary dynamics and population games
Authors:
Mabrok, Mohamed; Shamma, Jeff S. ( 0000-0001-5638-9551 )
Abstract:
Evolutionary dynamics describe how the population composition changes in response to the fitness levels, resulting in a closed-loop feedback system. Recent work established a connection between passivity theory and certain classes of population games, namely so-called “stable games”. In particular, it was shown that a combination of stable games and (an analogue of) passive evolutionary dynamics results in stable convergence to Nash equilibrium. This paper considers the converse question of necessary conditions for evolutionary dynamics to exhibit stable behaviors for all generalized stable games. Using methods from robust control analysis, we show that if an evolutionary dynamic does not satisfy a passivity property, then it is possible to construct a generalized stable game that results in instability. The results are illustrated on selected evolutionary dynamics with particular attention to replicator dynamics, which are also shown to be lossless, a special class of passive systems.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Mabrok MA, Shamma JS (2016) Passivity analysis of higher order evolutionary dynamics and population games. 2016 IEEE 55th Conference on Decision and Control (CDC). Available: http://dx.doi.org/10.1109/CDC.2016.7799211.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2016 IEEE 55th Conference on Decision and Control (CDC)
Issue Date:
5-Jan-2017
DOI:
10.1109/CDC.2016.7799211
ARXIV:
arXiv:1609.04952
Type:
Conference Paper
Sponsors:
Research supported by funding from KAUST.
Additional Links:
http://ieeexplore.ieee.org/document/7799211/
Appears in Collections:
Conference Papers; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorMabrok, Mohameden
dc.contributor.authorShamma, Jeff S.en
dc.date.accessioned2017-01-29T13:51:39Z-
dc.date.available2017-01-29T13:51:39Z-
dc.date.issued2017-01-05en
dc.identifier.citationMabrok MA, Shamma JS (2016) Passivity analysis of higher order evolutionary dynamics and population games. 2016 IEEE 55th Conference on Decision and Control (CDC). Available: http://dx.doi.org/10.1109/CDC.2016.7799211.en
dc.identifier.doi10.1109/CDC.2016.7799211en
dc.identifier.urihttp://hdl.handle.net/10754/622792-
dc.description.abstractEvolutionary dynamics describe how the population composition changes in response to the fitness levels, resulting in a closed-loop feedback system. Recent work established a connection between passivity theory and certain classes of population games, namely so-called “stable games”. In particular, it was shown that a combination of stable games and (an analogue of) passive evolutionary dynamics results in stable convergence to Nash equilibrium. This paper considers the converse question of necessary conditions for evolutionary dynamics to exhibit stable behaviors for all generalized stable games. Using methods from robust control analysis, we show that if an evolutionary dynamic does not satisfy a passivity property, then it is possible to construct a generalized stable game that results in instability. The results are illustrated on selected evolutionary dynamics with particular attention to replicator dynamics, which are also shown to be lossless, a special class of passive systems.en
dc.description.sponsorshipResearch supported by funding from KAUST.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/document/7799211/en
dc.subjectConvergenceen
dc.subjectGamesen
dc.subjectLinear systemsen
dc.subjectNash equilibriumen
dc.subjectSociologyen
dc.subjectStandardsen
dc.subjectStatisticsen
dc.titlePassivity analysis of higher order evolutionary dynamics and population gamesen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journal2016 IEEE 55th Conference on Decision and Control (CDC)en
dc.identifier.arxividarXiv:1609.04952en
kaust.authorMabrok, Mohameden
kaust.authorShamma, Jeff S.en
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