$offsymxref $offsymlist $ondotl *Kuhn-Tucker Theorem, Stackelberg Games, andAn Extended Mathematical *Programming (EMP)Framework in Trade (Part A) *Anton Yang Option limcol=0, limrow=0, solprint=off, decimals=6; Variable f1 Objective (original upper level problem) f2 Objective (original lower level problem) x y1 y2 lam1 lam2 ; Equation obj_f1 Objective Function f1 obj_f2 Objective Function f2 cons1 Constraint Solved from lower level by Kuhn-Tucker Theorem cons2 Constraint Solved from lower level by Kuhn-Tucker Theorem cons3 Constraint Solved from lower level by Kuhn-Tucker Theorem cons4 Constraint Solved from lower level by Kuhn-Tucker Theorem cons5 Constraint Solved from lower level by Kuhn-Tucker Theorem cons6 Constraint Solved from lower level by Kuhn-Tucker Theorem cons7 Constraint Solved from lower level by Kuhn-Tucker Theorem cons8 Constraint Solved from lower level by Kuhn-Tucker Theorem ; obj_f1.. f1 =e= -100*x - 1000*y1; obj_f2.. f2 =e= -y1 - y2; cons1.. -1 + lam1 + 2*lam2 =g= 0; cons2.. y1*(-1 + lam1 + 2*lam2) =e= 0; cons3.. -1 - lam1 + lam2 =g= 0; cons4.. y2*(-1 - lam1 + lam2) =e= 0; cons5.. -x - y1 + y2 + 1 =g= 0; cons6.. lam1*(-x - y1 + y2 + 1) =e= 0; cons7.. -2*y1 - y2 + 1 =g= 0; cons8.. lam2*(-2*y1 - y2 + 1) =e= 0; Model sinlevel /obj_f1, cons1, cons2, cons3, cons4, cons5, cons6, cons7, cons8/; y1.lo=0; y2.lo=0; lam1.lo=0; lam2.lo=0; Option nlp=baron, optcr=0.0001; Solve sinlevel using nlp minimizing f1; Display x.l, y1.l, y2.l, lam1.l, lam2.l, f1.l; $ontext x.fx = 1; Option nlp=baron; Solve sinlevel using nlp minimizing f1; Display x.l, y1.l, y2.l, lam1.l, lam2.l, f1.l; x.fx = 2.0005; Solve sinlevel using nlp minimizing f1; Display x.l, y1.l, y2.l, lam1.l, lam2.l, f1.l; $offtext