%%

function [Play Payouts tau] =PlayFingers(PayoutTables,Qas)
%
%  This function is called by FingerScript.m
%
%  It   uses a soft max policy to decide on the next board position
%
% Input:
%     PayoutTables: This is a cell. The jth entry of the cell is a matrix which gives
%           the payout to the jth player, given the play of the
%           participants.
%
%     Qas:   This is a cell. The jth entry corresponds to the jth player
%           and is comprised of two rows. The kth row contains the current estimate of
%           the value of playing k and the number of times that k has already been chosen
%           by the jth player.
%
% Output:
%
%    Play  is a vector. The jth entry is the choice made by the jth player.
%
%    Payouts is a vector. The jth entry contains the payout
%         to the jth player of the current game. This is actually implied
%         by the above variable Play (since PayoutTables is given).
%     
%    tau   is the temperature that is calculated in the program
%%
% 
% 
%    The algorithm is a softmax policy.
%

taumin=.3;    % Change Me; use .3 for Nash game
                  %  use .1 for Dominant, Prisoner's Dilemma Game

sPayoutTables = length(PayoutTables);
sQas          = length(Qas);

if sQas~=sPayoutTables
    display('sizes of PayoutTables and Qas not compatible');
    return
end

NumPlayers= sQas;

   
for jSubj=1:NumPlayers
    QasNow= Qas{jSubj};
    TotalPlayed1= QasNow(1,2 );        % Total Number of times 1 has been chosen
    TotalPlayed2= QasNow(2,2 );        % Total Number of times 2 has been chosen
    
    tau=3;
     %TotalPlayed= sum(Qas(indsPlayed,2 ));
   
    Q1= QasNow(1,1);        % This is the value of the first state for jSubj 
    Q2= QasNow(2,1);
    
    tau1= 3* min(1,500/TotalPlayed1);          % temperature depends on
    tau1=max(tau1,taumin);                  

    tau2= 3* min(1,500/TotalPlayed2);          % 
    tau2=max(tau2,taumin);
    
    tau=2/(1/tau1+1/tau2);

    QtauDiff= Q1/tau1 - Q2/tau2; 
    QtauDiff= (Q1 - Q2)/tau; 

    
    choice1= 1/(1 + exp(-QtauDiff) );   % This is the relative probabilities 
                                            %  of the first choice
    
    if rand()<choice1 % then the first choice picked
        choice=1;
    else
        choice=2;
    end
    Play(jSubj)=choice;
end

%%
%    calculate Payouts

for jSubj=1:NumPlayers
    POT = PayoutTables{jSubj};
  
    Payouts(jSubj) = POT(Play(1), Play(2)); 
end


%%