Replicator-Mutator Dynamics with Three Strategies

This Demonstration shows the phase portrait in an equilateral triangle of the replicator-mutator dynamics with three strategies. The parameters denote the payoff that an -strategist obtains in an interaction with a -strategist. The parameter denotes the total fraction of mutants or entrants in the population. The parameters denote the weights given by mutants to strategy , so is the fraction of mutants that adopt strategy . This Demonstration also calculates the critical points of the system and their corresponding eigenvalues, which are helpful in assessing the dynamic stability of the critical point.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Snapshot 1: system analyzed in [1]
Snapshot 2: if the payoff matrix is symmetric (which corresponds to the standard population-genetic model of natural selection on a large diploid population), a global Lyapunov function can be found that excludes cyclic behavior and guarantees that all orbits converge to the set of fixed points; see [2]
Snapshot 3: rock-scissors-paper game
Snapshot 4: strictly dominated strategies in the replicator-mutator dynamics can have an influence on the location of the limit rest points for small mutation; see [3]
[1] L. A. Imhof, D. Fudenberg, and M. A. Nowak, "Evolutionary Cycles of Cooperation and Deflection," in Proceedings of the National Academy of Sciences, 102(31), 2005 pp. 10797–10800.
[2] J. Hofbauer, "The Selection Mutation Equation," Journal of Mathematical Biology, 23, 1985 pp. 41–53,
[3] S. S. Izquierdo and L. R. Izquierdo, "Strictly Dominated Strategies in the Replicator-Mutator Dynamics," Games 2(3), 2011 pp. 355–364,


    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students. »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+