\$title Equilibrium model with and without containing bilevel (EQUIL_BILEVEL,SEQ=99) \$ontext Model to demonstrate that the agents in an equilibrium model are specified in the EMPinfo file and translated by JAMS in the same way whether they are: A. part of an equilibrium model (no outer optimizing agent) or B. part of an inner model (outer optimizing agent with bilevel) To show this we first create an equilibrium model with two VI agents, and then create a bilevel model whose inner problem reduces to the equilibrium model when the outer variables are fixed. The outer optimization is created so that solutions to the inner problem and equilibrium problem are the same, but in such a way that this depends on the implicit relationship between the inner and outer variables enforced by the VI agents. A casual inspection of the scalar models produced by JAMS is enough to demonstrate the similarity between the equilibrium and inner models. Contributor: Steven Dirkse, August 2013 \$offtext sets i / i1 * i2 / ii / 1 * 2 / j / j1 * j4 / k / k1 * k5 / t / t1 * t2 / ; alias(j,jj); parameters c(j) / j1 4 j2 -9 j3 6 j4 2 / b(i) / i1 2 i2 1 / bb(ii) / 1 -1 2 1 /; table Q(jj,jj) j1 j2 j3 j4 j1 4 -2 -1 -1 j2 -2 4 -2 -1 j3 -1 -2 4 -2 j4 -1 -1 -2 4 ; table A(i,j) j1 j2 j3 j4 i1 1 1 i2 1 1 1 ; table AA(ii,k) k1 k2 k3 k4 k5 1 1 1 1 2 1 1 1 ; table E(t,k) k1 k2 k3 k4 k5 t1 2 -1 2 2 t2 -1 3 3 3 ; scalars out1bar 'target value for out1 at outer obj solution' / 1 / v1bar "target value for v('j1') at out obj solution" d1 'dv1/dout1' / -0.5 / out2bar 'target value for out1 at outer obj solution' / 2 / w2bar "target value for w('k2') at out obj solution" d2 'dw2/dout2' / [5/6] / ; positive variable v(j); positive variable w(k); free variables out1 'var for outer min model' out2 'var for outer min model' s(t) ; equation F1(j) 'VI func perp to v'; equation g(i); equation F2(t) 'VI func perp to s'; equation sdef(t); equation h(ii); F1(j) .. sum{jj, Q(j,jj)*v(jj)} + c(j) =N= 0; g(i) .. sum {j, A(i,j)*v(j)} =G= b(i) - out1; F2(t) .. 2 * s(t) =N= 0; sdef(t) .. sum{k, E(t,k)*w(k)} =E= s(t); h(ii) .. sum {k, AA(ii,k)*w(k)} =G= bb(ii) + out2; v.up(j) = 20; v.up('j2') = 2; out1.fx = out1bar; out2.fx = out2bar; model equil / F1, g, F2, sdef, h /; file opt1 / 'jams.opt' /; putclose opt1 'EMPInfoFile empinfo1.txt' / 'fileName scalar1.gms' / 'dict dict1.txt' /; file empinfo1 / 'empinfo1.txt' /; putclose empinfo1 'equilibrium' / ' vi F1 v g' / / ' vi w F2 s sdef h' / ; equil.holdfixed = 1; equil.optfile = 1; option limrow=99, limcol=99; solve equil using emp; abort\$[equil.solvestat <> %solvestat.NormalCompletion%] 'equil not solved', equil.solvestat; v1bar = v.l('j1'); w2bar = w.l('k2'); scalars delta, o0, o1, odiff, marg; * this ontext/offtext block checks correctness of d1 := dv1/dout1 \$ontext delta = 0.01; o0 = v.l('j1'); out1.fx = out1bar + delta; solve equil using emp; abort\$[equil.solvestat <> %solvestat.NormalCompletion%] 'equil not solved', equil.solvestat; o1 = v.l('j1'); odiff = o1 - o0; marg = odiff / delta; display delta, o0, o1, odiff, marg, d1; \$exit \$offtext * this ontext/offtext block checks correctness of d1 := dv1/dout1 \$ontext delta = 0.01; o0 = w.l('k2'); out2.fx = out2bar + delta; solve equil using emp; abort\$[equil.solvestat <> %solvestat.NormalCompletion%] 'equil not solved', equil.solvestat; o1 = w.l('k2'); odiff = o1 - o0; marg = odiff / delta; display delta, o0, o1, odiff, marg, d2; \$exit \$offtext delta = 0.01; scalars ztarget, c_out1, c_v1, c_out2, c_w2; c_out1 = out1bar + delta; c_v1 = v1bar - (1/d1) * delta; c_out2 = out2bar + delta; c_w2 = w2bar - (1/d2) * delta; ztarget = sqr(delta) + sqr(delta/d1) + sqr(delta) + sqr(delta/d2); variable z 'outer objective'; equation zdef; zdef .. sqr(v('j1') - c_v1) + sqr(out1 - c_out1) + sqr(w('k2') - c_w2) + sqr(out2 - c_out2) =e= z; model bilev / F1, g, F2, sdef, h zdef /; file opt2 / 'jams.op2' /; putclose opt2 'EMPInfoFile empinfo2.txt' / 'fileName scalar2.gms' / 'dict dict2.txt' /; file empinfo2 / 'empinfo2.txt' /; putclose empinfo2 'bilevel' / ' vi F1 v g' / / ' vi w F2 s sdef h' / ; out1.lo = out1bar - 1; out1.up = out1bar + 1; out1.lo = -INF; out1.up = INF; out2.lo = out2bar - 1; out2.up = out2bar + 1; out2.lo = -INF; out2.up = INF; bilev.optfile = 2; solve bilev using emp min z; abort\$[bilev.solvestat <> %solvestat.NormalCompletion%] 'bilev not solved', bilev.solvestat; scalars v1, w2 tol / 1e-5 /; v1 = v.l('j1'); w2 = w.l('k2'); display z.l, ztarget, out1.l, out1bar, v1, v1bar, out2.l, out2bar, w2, w2bar; abort\$[abs(z.l - ztarget) > tol] 'bilevel objective not as expected', z.l, ztarget; abort\$[abs(out1.l - out1bar) > tol] 'variable out1 not as expected', out1.l, out1bar; abort\$[abs(out2.l - out2bar) > tol] 'variable out2 not as expected', out2.l, out2bar; * uncommment these to keep all the intermediate files around execute 'rm -f scalar1.??? scalar2.??? dict1.txt dict2.txt empinfo1.txt empinfo2.txt' execute 'rm -f scalar?pf.pf jams.opt jams.op2'