Saving results at Nash equilibrium

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SUMMARY

This discussion focuses on implementing power control in telecommunications using game theory to achieve Nash equilibrium. The utility function defined is u=L*R*f/(M*pj)-c*pj, where f=(1-2*pe)^M, with pe representing Bit Error Rate and g as Signal to Interference Ratio. The code provided iterates through various power levels (pj) and cost levels (c) to compute utilities and find the maximum utilities at equilibrium. The final goal is to save these utilities and visualize the results through graphing.

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  • Understanding of game theory principles, particularly Nash equilibrium.
  • Familiarity with telecommunications concepts such as Bit Error Rate and Signal to Interference Ratio.
  • Proficiency in MATLAB for implementing the provided code and performing simulations.
  • Knowledge of utility functions and optimization techniques in a multi-agent context.
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  • Explore MATLAB's plotting functions to visualize utility results effectively.
  • Research advanced game theory strategies for optimizing power control in wireless networks.
  • Learn about the impact of varying Bit Error Rates on utility functions in telecommunications.
  • Investigate alternative algorithms for achieving efficient equilibria in multi-player scenarios.
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Telecommunications engineers, game theorists, and researchers focused on optimizing wireless network performance through power control strategies.

Jmo2005
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My code is about power control via game theory.
I want to save players' utilities @ Nash equilibrium.
Ok, the problem is about telecommunications.
Specifically, it is efficient power control via pricing in wireless data networks.
There is a utility function (u=L*R.*f./(M.*pj)-c.*pj)
f is the efficiency function (f=(1-2.*pe).^M)
pe is the Bit Error Rate
and g is the Signal to Interference Ratio
k is a constant equal to 7,75*10^(-3)
M is total number of bits per frame
L is number of information bits per frame
W is spread spectrum bandwidth
R is bit rate
s^2 is noise at the receiver
h=k./(d.^4) is simply the gain of the route
and pmax is the maximum powwer constraint for every player
d=[0.31 0.46 0.57 0.66 0.74 0.81 0.88 0.94 1.00] is the list of distances that players have from the terminal
We try all power levels pj=0.001:0.00001:pmax for every player and compute signal, interference and then utility, trying to find the best response.
We also try all cost levels c=10^3:10^4:10^10^5 for every power level, for every player at every trial to find the best response via pricing, as the previous process does not results to an efficient equilibrium!
The general idea is to find the maximum utilities and save them.All I have to do now is the last part which is saving utilities at equilibrium and make a graph of the results!I know that you might still not have a clear picture, but I just tried to describe you the concept...
Any help is welcome and even a little bit of code that is not correct, just to give me an idea of how to do these things...Thanks in advance!

Here is my code:

close all;
clear all;


L=64;
R=10^4;
M=80;
W=10^6;
s2=5*10^(-15);
pmax=2;
k=0.097*10^(-3);
pj=0.001:0.00001:pmax;
d=[0.31 0.46 0.57 0.66 0.74 0.81 0.88 0.94 1.00];
h=k./(d.^4);
ind=1;
ind2=1;
p(ind,:)=ones(1,9);
q=zeros(1,9);
for c=10^3:10^4:10^10^5;
c
while max(abs(p(ind,:)-q))>10^(-4)
q=p(ind,:)
ind=ind+1;
for i=1:9
g=(W/R)*(h(i)*pj)/(sum(h(1:(i-1)).*p(ind-1,1:(i-1)))+sum(h((i+1):end).*p(ind-1,(i+1):end)) + s2);
pe=0.5.*exp(-g./2);
f=(1-2.*pe).^M;
u=L*R.*f./(M.*pj)-c.*pj;
um=max(u);
kk=find(u==um);
p(ind,i)=pj(kk);

end

end
pfin(ind2,:)=p(ind,:);
ind2=ind2+1;
ind=1;
clear p
p(ind,:)=ones(1,9);

end
 
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