Asymmetric evolutionary games/Environmental feedback

Author: Christoph Hauert

This tutorial complements a research article by Christoph Hauert, Camille Saade & Alex McAvoy

Environmentally-induced asymmetric games

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Asymmetric donation game

\[\begin{matrix}~&\begin{matrix}\ \ C_r\quad & C_p\quad & D_r\quad & D_p\quad\end{matrix} \\ \begin{matrix}C_r\\C_p\\D_r\\D_p\end{matrix}& \begin{pmatrix} b_r-c_r & b_p-c_r & -c_r & -c_r \\ b_r-c_p & b_p-c_p & -c_p & -c_p \\ b_r & b_p & 0 & 0 \\ b_r & b_p & 0 & 0 \\ \end{pmatrix}\end{matrix}. \]

Evolutionary dynamics

Constant, heterogeneous environment

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Asymmetric 2×2 game

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Asymmetric Donation game

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Asymmetric Snowdrift game - equal split

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Asymmetric Snowdrift game - fair split

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Environmental feedback without interactions

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Conservation game

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Feedback & games

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Asymmetric Donation game with positive environmental feedback

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Asymmetric Snowdrift game with positive environmental feedback

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Socio-environmental dilemmas

negative environmental feedback

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Asymmetric Donation game - limit cycles

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Asymmetric Snowdrift game - stable focus

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Asymmetric Harmony game - bistability, mixed

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Dynamical equations

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References

1. Hauert, C., Saade, C. & McAvoy, A. (2018) Asymmetric Evolutionary Games with Environmental Feedback. J. theor. Biol. XXX XXX doi: XXX.