Passivity analysis of higher order evolutionary dynamics and population games
Type
Conference PaperAuthors
Mabrok, MohamedShamma, Jeff S.

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
Date
2017-01-05Preprint Posting Date
2016-09-16Online Publication Date
2017-01-05Print Publication Date
2016-12Permanent link to this record
http://hdl.handle.net/10754/622792
Metadata
Show full item recordAbstract
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.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.Sponsors
Research supported by funding from KAUST.arXiv
1609.04952Additional Links
http://ieeexplore.ieee.org/document/7799211/ae974a485f413a2113503eed53cd6c53
10.1109/CDC.2016.7799211