Notes
The replicator dynamics describes the change in \(x_{i}\), the frequency of trait i, with the following equation:
$$\dot{x} = x_{i} [w_{i} - \bar{w}]$$where \(w_{i}\) is the fitness of trait i and \(\bar{w}\) is the average fitness in the population, which both depend on the current population composition.
Assuming only selection is at work (e.g., using the replicator dynamics with standard assumptions about population structure, etc.) and that the possible phenotypes correspond to pure strategies of the game.
References
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Skyrms, B. 1990. The dynamics of rational deliberation. Cambridge: Harvard University Press.
Sober, E. 1984. The nature of selection: Evolutionary theory in philosophical focus. Chicago: University of Chicago Press.
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Acknowledgements
Thanks to Simon Huttegger and Mike Schneider for helpful feedback, and to Corey Dethier, Emanuele Ratti, Lynn Joy, Justin Bruner, Brian Skyrms, and Elliott Chen for joining me in discussions on the book.
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Rubin, H. The rationality of mother nature. Metascience 28, 365–372 (2019). https://doi.org/10.1007/s11016-019-00452-8
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DOI: https://doi.org/10.1007/s11016-019-00452-8