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

	   John Rust, University of Maryland, November 2005 */

   proc (2)=br_a(p_b,x_a);  /* x_a is player a's observable type and
                               p_b is player a's belief about the 
			       probablity that prisoner b will confess.
			       Procedure returns the probability that
			       prisoner a will confess, representing
			       the optimal decision rule for prisoner
			       a whether to confess or not confess,
			       with prisoner a's private information
			       "integrated out".
			       
			       Implicitly passed global:
			       
			       sig_a: scale parameter for prisoner a'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_b  */

       local df,p;
/*
       p=1/(1+exp((eu_a(0,x_a,p_b)-eu_a(1,x_a,p_b))/sig_a));
       df=u_a(0,1,x_a)-u_a(0,0,x_a)-u_a(1,1,x_a)+u_a(1,0,x_a);
       df=-p*(1-p)*df/sig_a;
*/
       p=1/(1+exp(qa[1]*x_a+qa[2]*x_a*p_b));
       df=-p*(1-p)*qa[2]*x_a;

       retp(p,df);

   endp;