%  March 20th 2008
%  Written by PRBaldwin
%%
%   Part 1. Set up the Payout Matrix
%   Part 2. Play the Finger Game
%   Part 3. Assess Results
%%
%   Part 1.

% Payout2A= [1 -1; -1 1]; % symmetrical, Nash
  Payout2A = [2 -3; -3 4]; % Nash
  Payout2A = [0 -2; 2 0] ; % antisymmetric, dominant
  Payout2A = [1 -2;  2 0] ; % Bluefin in peril
  Payout2B = [1  2; -2 0] ; % Bluefin in peril

% Payout2B=- Payout2A;

PayoutTables{1}= Payout2A;
PayoutTables{2}= Payout2B

NumPlayers=length(PayoutTables);

%%  Part 2
%
%   Play The Game

NumRounds2Play=40000;

clear Qas
for jSubj=1:2
    Qas{jSubj} =2*( rand(2,1)-.5); % Between -1 and 1
                                % Has as many entries as there are possible
                                % moves
    Qas{jSubj} =[Qas{jSubj},ones(2,1)];   % Keep track of the number of updates
end

%   
for NumRound=1:NumRounds2Play

    if round(NumRound/1000)*1000==NumRound, NumRound, end % just print

     [Play Payouts tau] =  PlayFingers(PayoutTables,Qas);

    NewQas=UpdateQFinger(Play,Payouts,Qas);
    Qas=NewQas;

end

%%  Part 3
%   Summarize results



for jSubj=1:NumPlayers
%     
%     prob1(jSubj)= Qas{jSubj}(1,2)/ sum(Qas{jSubj}(:,2)) ;
%     prob1(jSubj) = round(1000*prob1(jSubj))/1000;
%     display(strcat('prob of playing 1 by Player', num2str(jSubj),'=',num2str(prob1(jSubj))))
%    
%     
%     display(' ')
%     prob2(jSubj)= Qas{jSubj}(2,2)/ sum(Qas{jSubj}(:,2)) ;
%     prob2(jSubj) = round(1000*prob2(jSubj))/1000;
%     display(strcat('prob of playing 2 by Player', num2str(jSubj),'=',num2str(prob2(jSubj))))
    
    display(' ')
    prob1tau(jSubj)= exp(Qas{jSubj}(1,1)/tau)/ sum(exp(Qas{jSubj}(:,1)/tau)) ;
    prob1tau(jSubj) = round(1000*prob1tau(jSubj))/1000;
    display(strcat('prob (based on tau) of playing 1 by Player', ...
         num2str(jSubj),'=',num2str(prob1tau(jSubj))))
    
    display(' ')
    prob2tau(jSubj)= exp(Qas{jSubj}(2,1)/tau)/ sum(exp(Qas{jSubj}(:,1)/tau)) ;
    prob2tau(jSubj) = round(1000*prob2tau(jSubj))/1000;
    display(strcat('prob (based on tau) of playing 2 by Player', ...
    num2str(jSubj),'=',num2str(prob2tau(jSubj))))

    display(' ')
end    


% tau*log(prob1./(1-prob1))
% tau*log(prob2./(1-prob2))
% 
% Qas{1}(1,1)-Qas{1}(2,1)
% 
% mean(jSubj)
% 7/12