/* EQUILPLOT.GPR: program to plot equilibriun of prisoner's dilemma game

		  John Rust, University of Maryland, November 2005 */
   library pgraph;
   pqgwin many;

   #include setup.gpr;

   nplot=50;

   x=seqa(0,1/nplot,nplot+1);

   y=zeros(rows(x),1);
   y1=y;
   y2=y;

   xa=1;
   xb=1;

   i=1; do until i > rows(x);

      {y[i],df}=br2_a(xa,xb,x[i]);
      {y1[i],df}=br_b(y[i],xb);
      {y1[i],df}=br_a(y1[i],xa);
      {y2[i],df}=br_a(x[i],xa);

   i=i+1; endo;


   graphset;
   fonts("simplex simgrma");
   _pdate="";
   _pgrid=0|0;
   _pltype=6|3|6|1;
   _plwidth=5|5;
   xtics(0,1,.1,0);
   ytics(0,1,.1,0);
   axmargin(1,3.25,1,1);
   title("Bayesian Nash Equilibria\LPrisoner's Dilemma Game x]a[="$+
       ftos(xa,"-*.*lf",4,2)$+" x]b[="$+ftos(xb,"-*.*lf",4,2));
   xlabel("Probability prisoner a confesses");
   ylabel("Probability prisoner a confesses");

   _plegctl=1~4~.55~.15;
   _plegstr="45 degree line\000\202l\201[2]]a]\000\202l\201[4]]a[\000\202l\201]b[";



#IFUNIX
  let cv = 100 100 640 480 0 0 1 6 15 0 0 2 2;
  wxy = WinOpenPQG(cv,"Equilibrium of Prisoner's Dilemman Game","");
  call WinSetActive(wxy);
#ENDIF

  xy(x,x~y~y1~y2);

#IFUNIX
  call WinSetActive(1);
#ENDIF

   y=zeros(rows(x),1);
   y1=y;

   i=1; do until i > rows(x);

      {y[i],df}=br_b(x[i],xb);
      y1[i]=ibr_a(x[i],xa);

   i=i+1; endo;

   {pa,pb}=equil(xa,xb);
   

   graphset;
   fonts("simplex simgrma");
   _pdate="";
   _pgrid=0|0;
   _pltype=6|6;
   _plwidth=5|5;
   xtics(0,1,.1,0);
   ytics(0,1,.1,0);
   axmargin(1,3.25,1,1);
   title("Bayesian Nash Equilibria\LPrisoner's Dilemma Game x]a[="$+
       ftos(xa,"-*.*lf",4,2)$+" x]b[="$+ftos(xb,"-*.*lf",4,2));
   xlabel("Probability prisoner a confesses");
   ylabel("Probability prisoner b confesses");

   _plegctl=1~6~.05~.75;
   _plegstr="\202l\201]b[\000\202l\201]a[";
   _pline=(1~3~pa~0~pa~pb~1~4~3);
   _pline=_pline|(1~3~0~pb~pa~pb~1~4~3);



#IFUNIX
  let cv = 100 100 640 480 0 0 1 6 15 0 0 2 2;
  wxy = WinOpenPQG(cv,"Equilibrium of Prisoner's Dilemman Game","");
  call WinSetActive(wxy);
#ENDIF

  xy(x,y~y1);

#IFUNIX
  call WinSetActive(1);
#ENDIF

   yy=zeros(rows(x),1);
   yy1=zeros(rows(x),1);

   i=1; do until i > rows(x);

      yy[i]=eu_a(1,xa,x[i]);
      yy1[i]=eu_a(0,xa,x[i]);

   i=i+1; endo;

   graphset;
   _pdate="";
   _pgrid=0|0; 
   _pltype=6|3;
   _plwidth=5|5;
   title("Expected Payoffs to Prisoner A\LPrisoner's Dilemma Game x]a[="$+
       ftos(xa,"-*.*lf",4,2)$+" x]b[="$+ftos(xb,"-*.*lf",4,2));
   xlabel("Probability prisoner b confesses");
   ylabel("Expected utility for prisoner A");

   _plegstr="Confess\000Don't Confess";
   _plegctl=2~5~1~1;


#IFUNIX
  let cv = 100 100 640 480 0 0 1 6 15 0 0 2 2;
  wxy = WinOpenPQG(cv,"Expected Payoffs in Prisoner's Dilemma Game","");
  call WinSetActive(wxy);
#ENDIF

  scale(x,yy~yy1);
  xy(x,yy~yy1);

#IFUNIX
  call WinSetActive(1);
#ENDIF

   yy=zeros(rows(x),1);
   yy1=zeros(rows(x),1);

   i=1; do until i > rows(x);

      yy[i]=eu_b(1,xb,x[i]);
      yy1[i]=eu_b(0,xb,x[i]);

   i=i+1; endo;

   graphset;
   _pdate="";
   _pgrid=0|0;
   _pltype=6|3;
   _plwidth=5|5;
   xtics(0,1,.1,0);
   title("Expected Payoffs to Prisoner B\LPrisoner's Dilemma Game x]a[="$+
       ftos(xa,"-*.*lf",4,2)$+" x]b[="$+ftos(xb,"-*.*lf",4,2));
   xlabel("Probability prisoner a confesses");
   ylabel("Expected utility for prisoner B");

   _plegstr="Confess\000Don't Confess";
   _plegctl=2~5~1~1;


#IFUNIX
  let cv = 100 100 640 480 0 0 1 6 15 0 0 2 2;
  wxy = WinOpenPQG(cv,"Expected Payoffs in Prisoner's Dilemma Game","");
  call WinSetActive(wxy);
#ENDIF

  scale(x,yy~yy1);
  xy(x,yy~yy1);

#IFUNIX
  call WinSetActive(1);
#ENDIF

  z=zeros(rows(x),rows(x));
  z1=zeros(rows(x),rows(x));
  i=1; do until i > rows(x);
    j=1; do until j > rows(x);

       {pa,pb}=equil(x[i],x[j]);

       z[i,j]=pa;
       z1[i,j]=pb;

    j=j+1; endo;
  i=i+1; endo;


   graphset;
   _pdate="";
   _pgrid=0|0;
   _pltype=6|6;
   _plwidth=5|5;
   xtics(0,1,.1,0);
   ytics(0,1,.1,0);
   ztics(.5,1,.1,0); 
   title("Equilibrium Probability A confesses\LPrisoner's Dilemma Game");
   xlabel("Prisoner a's x]a[ value");
   ylabel("Prisoner b's x]b[ value");

#IFUNIX
  let cv = 100 100 640 480 0 0 1 6 15 0 0 2 2;
  wxy = WinOpenPQG(cv,"Expected Payoffs in Prisoner's Dilemma Game","");
  call WinSetActive(wxy);
#ENDIF

  surface(x',x,z');

#IFUNIX
  call WinSetActive(1);
#ENDIF

   graphset;
   _pdate="";
   _pgrid=0|0;
   _pltype=6|6;
   _plwidth=5|5;
   xtics(0,1,.1,0);
   ytics(0,1,.1,0);
   ztics(.5,1,.1,0); 
   title("Equilibrium Probability B confesses\LPrisoner's Dilemma Game");
   xlabel("Prisoner a's x]a[ value");
   ylabel("Prisoner b's x]b[ value");

#IFUNIX
  let cv = 100 100 640 480 0 0 1 6 15 0 0 2 2;
  wxy = WinOpenPQG(cv,"Expected Payoffs in Prisoner's Dilemma Game","");
  call WinSetActive(wxy);
#ENDIF

  surface(x',x,z1');

#IFUNIX
  call WinSetActive(1);
#ENDIF