/* IBR_B.G: inverse best response function for player b (column player) in the
            prisoners dilemma game

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

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

	   John Rust, University of Maryland, November 2005 */

   proc (1)=ibr_b(p_b,x_b);  /* x_b is player a's observable type and
                               p_a is player b's belief about the 
			       probablity that prisoner a will confess.
			       Procedure returns the probability that
			       prisoner b will confess, representing
			       the optimal decision rule for prisoner
			       a whether to confess or not confess,
			       with prisoner b's private information
			       "integrated out".
			       
			       Implicitly passed global:
			       
			       sig_b: scale parameter for prisoner b's
			              private information (Type III
				      extreme value distribution) 

                               returned values:

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

       local df,p,pbu,pbl;

       {pbl,df}=br_b(0,x_b);
       {pbu,df}=br_b(1,x_b);

       if (p_b < pbl);

           retp(0);

       elseif (p_b > pbu);

           retp(1);

       else;

           df=ln(1-1/p_b)-(dd_b-cd_b)*x_b;
	   retp(df/(x_b*(dc_b-cc_b+cd_b-dd_b)));

       endif;


   endp;