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

	   John Rust, University of Maryland, November 2005 */

   proc (2)=br_b(p_a,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:  best response probability (of confessing)
			       df: derivative of best response
			           probability with respect to p_a
				      
				      */

       local df,p;
/*
       p=1/(1+exp((eu_b(0,x_b,p_a)-eu_b(1,x_b,p_a))/sig_b));
       df=u_b(0,1,x_b)-u_b(0,0,x_b)-u_b(1,1,x_b)+u_b(1,0,x_b);
       df=-p*(1-p)*df/sig_b;
*/
       p=1/(1+exp(qb[1]*x_b+qb[2]*x_b*p_a));
       df=-p*(1-p)*qb[2]*x_b;

       retp(p,df);

   endp;