Hello there,(adsbygoogle = window.adsbygoogle || []).push({});

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 afitness function[itex]F_{x_i}[/itex] for each strategy.

I have theaverage fitnessof the population [itex]\bar{F} = \sum_{i = 1}^8{x_i(F_{x_i})}[/itex].

Finally I have thereplicator 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 functionsolve, 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**