The Cooperation Ceiling: Extrinsic Population Dynamics and the Intrinsic Escape

2026-07-01

Another new preprint (it has been a productive year!): "The Cooperation Ceiling: Extrinsic Population Dynamics and the Intrinsic Escape".

In evolutionary game theory, one of the main tools used for understanding the spread of behaviour is something called a population dynamic. This is a model of how individuals change over time. Some of these work in an extrinsic way: individuals look around and see how well others are doing and change their behaviour to match. Some of these work in an intrinsic way: individuals think about what would work for them.

In this paper, we show that for Social dilemmas (think Prisoners' Dilemma, Public Goods Game etc) extrinsic population dynamics have a ceiling of the amount of cooperation that can emerge. Importantly, this is not a ceiling for intrinsic processes.

There is a nice theorem with a rigorous proof showing this but other important contributions of this paper include a formal definition of an extrinsic population dynamic as well we a bunch of nice diagrams and plots.

@misc{foster2026cooperationceilingextrinsicpopulation,
      title={The Cooperation Ceiling: Extrinsic Population Dynamics and the Intrinsic Escape}, 
      author={Harry Foster and Vince Knight and Sebastian Krapohl},
      year={2026},
      eprint={2606.31740},
      archivePrefix={arXiv},
      primaryClass={cs.GT},
      url={https://arxiv.org/abs/2606.31740}, 
}