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*Kuhn-Tucker Theorem, Stackelberg Games, andAn Extended Mathematical
*Programming (EMP)Framework in Trade (Part A)

*Anton Yang

Option limcol=0, limrow=0, decimals=6;

Variable f1 Objective (original upper level problem)
         f2 Objective (original lower level problem)
;

Nonnegative Variables
         x
         y1
         y2
;

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
;


obj_f1..
      f1 =e= -100*x - 1000*y1;

obj_f2..
      f2 =e= -y1 - y2;

cons1..
      -x - y1 + y2 =g= -1;

cons2..
      -2*y1 - y2 =g= -1;

Model Bilevel /all/;

$echo bilevel x min f2 y1 y2 obj_f2 cons1 cons2 > "%emp.info%"
Solve Bilevel using EMP minimizing f1;