Speaker
Description
Several game-theoretic models such as oligopoly, war of attrition, and international trade, are inherently asymmetric (role dependent). However, in contrast to symmetric games (role independent), relatively limited research has been devoted to the evolutionary analysis of asymmetric games. Systematic attention to these games emerged over the last four to five decades.
For asymmetric games with finite strategy sets, the pioneering evolutionary analysis was initiated in \cite{selten1980}, followed by further developments by other authors. In the context of asymmetric games with continuous strategy sets, the work in \cite{PalaciosandLerma2015} is particularly significant, as it provides an elegant evolutionary framework of such games using replicator dynamics (a type of population dynamics). Subsequently, other researchers also contributed to the evolutionary study of asymmetric continuous games.
In our work (see e.g., \cite{narang2019}, \cite{narang2021}, \cite{narang2022}), we introduced and generalized several stability concepts for population profiles and sets of profiles in asymmetric continuous games with the associated replicator dynamics. In particular, we established results connecting static stability notions such as strong uninvadability, strong unbeatability, strong immutability, strong immovability, and neighborhood strong superiority with dynamic stability properties like Lyapunov stability, asymptotic stability, weak attraction, and neighborhood attraction.
Bibliography
@article{PalaciosandLerma2015,
title={Evolutionary dynamics on measurable strategy spaces: Asymmetric games},
author={Mendoza-Palacios, Saul and Hern{\'a}ndez-Lerma, On{\'e}simo},
journal={Journal of Differential Equations},
volume={259},
number={11},
pages={5709--5733},
year={2015}
}
@article{selten1980,
title={A note on evolutionarily stable strategies in asymmetric animal conflicts},
author={Selten, Reinhard},
journal={Journal of Theoretical Biology},
volume={84},
number={1},
pages={93--101},
year={1980}
}
@article{narang2019,
title={Evolutionary stability of polymorphic profiles in asymmetric games},
author={Narang, Aradhana and Shaiju, A. J.},
journal={Dynamic Games and Applications},
volume={9},
number={4},
pages={1126--1142},
year={2019}
}
@article{narang2021,
title={Stability of faces in asymmetric evolutionary games},
author={Narang, Aradhana and Shaiju, A. J.},
journal={Annals of Operations Research},
volume={304},
pages={343–359},
year={2021}
}
@article{narang2022,
title={Neighborhood strong superiority and evolutionary stability of polymorphic profiles in asymmetric games},
author={Narang, Aradhana and Shaiju, A. J.},
journal={Journal of Dynamics and Games},
volume={9(3)},
pages={253-266},
year={2022}
}
