/* IBR_A.G: inverse best response function for player a (row player) in the
            prisoners dilemma game

	    This procedure returns the value of p_b (a's beliefs of
	    prisoner b's probability of confessing) necessary to
	    "rationalize" a given value of a confessing, p_a.

	    p_a lives on a subdomain of [0,1], since ordinarily p_a 
	    cannot assume all possible values in this interval.

	   John Rust, University of Maryland, November 2005 */

   proc (1)=ibr_a(p_a,x_a);  /* x_a is player a's observable type and
                               p_a is player a's best response probability
			       Procedure returns the probability that
			       prisoner a believes that prisoner b will 
			       confess, that is sufficient to cause him/her
			       to confess with probability p_a.
			       
			       Implicitly passed global:
			       
			       sig_a: scale parameter for prisoner a's
			              private information (Type III
				      extreme value distribution) 

                               returned values:

			       p:  inverse best response probability (of confessing)
				      
				      */

       local df,p,pau,pal;

       {pal,df}=br_a(0,x_a);
       {pau,df}=br_a(1,x_a);

       if (p_a < pal);

           retp(0);

       elseif (p_a > pau);

           retp(1);

       else;

           df=ln(1-1/p_a)-(dd_a-cd_a)*x_a;
	   retp(df/(x_a*(dc_a-cc_a+cd_a-dd_a)));

       endif;


   endp;