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MATLAB Critical points of system of ODE in MATLAB - Game theory and poker

  1. Nov 2, 2013 #1
    Hello there,

    I hope I'm posting in the right section.

    I have been doing some work on evolutionary game theory and poker. I will give a brief description of how I got here.

    I have eight strategies [itex]i = 1, 2, \ldots, 8[/itex] and the eight proportions of the population playing each strategy is [itex]x_1, x_2, \ldots , x_8[/itex].

    I also have a fitness function [itex]F_{x_i}[/itex] for each strategy.
    I have the average fitness of the population [itex]\bar{F} = \sum_{i = 1}^8{x_i(F_{x_i})}[/itex].
    Finally I have the replicator equations [itex]\frac{dx_i}{dt} = x_i(F_{x_i}-\bar{F})[/itex].

    I now want to find the critical points of the system containing the eight replicator equations. So I set [itex]\frac{dx_i}{dt} = 0[/itex] for all [itex]i = 1, 2, \ldots ,8[/itex]. I have tried this using MATLABs function solve, and after much trial and error the best result was a parametric solution in 6 of the eight variables [itex]x_1, x_2, \ldots x_8[/itex] and my instructor was quite confided that I would only find a single non-trivial solution.

    If anyone have advice on how I can solve the problem it would be great. I am not that good with MATLAB. I also would like to specify that [itex]x_i > 0[/itex] for all [itex]i[/itex].

    OBS: I have all the fitness functions, and they are all functions of all eight variables [itex]x_i[/itex], and they are all linear, but the average fitness [itex]\bar{F}[/itex] and the replicator equations aren't.

    Thanks in advance!
  2. jcsd
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