TY - GEN
T1 - Passivity analysis of higher order evolutionary dynamics and population games
AU - Mabrok, Mohamed
AU - Shamma, Jeff S.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Research supported by funding from KAUST.
PY - 2017/1/5
Y1 - 2017/1/5
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/622792
UR - http://ieeexplore.ieee.org/document/7799211/
UR - http://www.scopus.com/inward/record.url?scp=85010799397&partnerID=8YFLogxK
U2 - 10.1109/CDC.2016.7799211
DO - 10.1109/CDC.2016.7799211
M3 - Conference contribution
SN - 9781509018376
SP - 6129
EP - 6134
BT - 2016 IEEE 55th Conference on Decision and Control (CDC)
PB - Institute of Electrical and Electronics Engineers (IEEE)
ER -