Saving results at Nash equilibrium

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In summary, the conversation discussed a code for power control using game theory in telecommunications. The goal was to achieve efficient power control through pricing in wireless data networks, taking into account factors such as utility function, efficiency function, Bit Error Rate, Signal to Interference Ratio, and power constraints. The process involved trying different power levels and cost levels to find the best response and ultimately maximize utilities. The final step was to save the utilities at equilibrium and create a graph of the results. The speaker also welcomed any additional help or code suggestions.
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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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Anyone?
 

1. What is a Nash equilibrium?

A Nash equilibrium is a concept in game theory that represents a stable state in which no player has an incentive to unilaterally change their strategy. In other words, each player's strategy is the best response to the other players' strategies, and no player can improve their outcome by changing their strategy while the others keep theirs.

2. Why is it important to save results at Nash equilibrium?

Saving results at Nash equilibrium can provide valuable insights into the dynamics of a game and help us understand how players behave and make decisions. It can also be used to predict outcomes and inform decision-making in various fields, such as economics, politics, and biology.

3. How do you determine the Nash equilibrium in a game?

The Nash equilibrium can be determined by analyzing the payoffs of each player's strategies and identifying the point at which no player has an incentive to deviate from their current strategy. This can be done through mathematical calculations or by using graphical representations, such as payoff matrices.

4. Can there be multiple Nash equilibria in a game?

Yes, a game can have multiple Nash equilibria. This can happen when there are multiple strategies that are equally good responses to the other players' strategies. In these cases, it may be difficult to predict which equilibrium will occur in a real-world scenario.

5. What factors can affect the stability of a Nash equilibrium?

The stability of a Nash equilibrium can be affected by changes in the game's rules or payoffs, the number of players, and the level of uncertainty or risk involved. It can also be influenced by external factors, such as social norms and communication among players.

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