October  2020, 7(4): 365-386. doi: 10.3934/jdg.2020028

Replicator dynamics: Old and new

Institut de Mathématiques Jussieu-PRG, Sorbonne Université, Campus P. & M. Curie, CNRS UMR 7586, 4 Place Jussieu, 75005 Paris, France

Received  October 2019 Published  September 2020

Fund Project: Part of this work was presented at "Journées Franco-Chiliennes d'Optimisation", Toulouse, July 2017, and dedicated to the memory of Felipe Alvarez. This research was partially supported by a PGMO grant COGLED. The author thanks Josef Hofbauer for many constructive comments and a referee for an extremely precise and helpful report

We introduce the unilateral version associated to the replicator dynamics and describe its connection to on-line learning procedures, in particular to the multiplicative weight algorithm. We show the interest of handling simultaneously discrete and continuous time analysis.

We then survey recent results on extensions of this dynamics as maximization of the cumulative outcome with alternative regularization functions and variable weights. This includes no regret algorithms, time average version and link to best reply dynamics in two person games, application to equilibria and variational inequalities, convergence properties in potential and dissipative games.

Citation: Sylvain Sorin. Replicator dynamics: Old and new. Journal of Dynamics & Games, 2020, 7 (4) : 365-386. doi: 10.3934/jdg.2020028
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[29]

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Table1 
0 1 -1
-1 0 1
1 -1 0
0 1 -1
-1 0 1
1 -1 0
Table2 
0 0
0 0
0 0
0 0
0 0
0 0
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