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leap_sm.c
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#define EULER 0.577215664901532
void leap_sm(MPstruct mp, Gamestruct* g, Bnestruct bne, Brstruct* br, int* eqstring, int ic1z, int ic2z, int iCz) {
/********************************************************/
// SECTION 1: DECLARATIONS
/********************************************************/
// Params and Modparams
int nC; //Main parameter
MVstruct mv;
//double v, v1, r, p1;
int i, j, iC, jp, jC, ic1, ic2, ieqb, neqb;
int i1, i2, iccc;
//double q; //temps for c>0
//double v, v1, r, p1;
//int i, j, iF, iI, iC, ic1, ic2, ieqb, it, ip, neqb;
double v, q;
double* hc1;
double* hc2;
Brc_amstruct brc;
double EP10, EP11, EP20, EP21, logsum1, logsum2, p1, p2, f1;//constants for symbolic solutions in cost recursions
double AN1,AI1,B,AN2,AI2;
#ifdef PRINTnrstagempe
int neqstr; //only for output of ESR for a given number of stage equilibria
#endif
nC = mp.nC; // very much used => for easy referencing
/********************************************************/
// SECTION 2: MEMORY ALLOCATION
/********************************************************/
mv.h1 = (double *) calloc(nC*nC, sizeof(double)); // temp storage of formula parts, precomputing, see c>0
mv.h2 = (double *) calloc(nC*nC, sizeof(double)); // temp storage of formula parts, precomputing, see c>0
hc1 = (double *) calloc(nC*nC, sizeof(double)); // temp storage of formula parts, precomputing, see c>0
hc2 = (double *) calloc(nC*nC, sizeof(double)); // temp storage of formula parts, precomputing, see c>0
mv.eqbinfo = (double *) calloc(5*MAXEQBINFO, sizeof(double)); // storage for found equilibria in findeqb
/********************************************************/
// SECTION 3: LOOP OVER iC
/********************************************************/
for (iC=iCz;iC<nC;iC++) {
/********************************************************/
// Initialize for iC
/********************************************************/
g[iC].c[0]=mp.cgrid[iC]; // save value of c in output
mv.pc=f_pti(iC,&mp); // probability of a technological improvement. Initially improvements are assumed to be
// 'incremental', that is the jump, if it occurs, is to c'=cgrid(i-1) with probability pti
// for iC=0 pti=0!
mv.kv=f_kf(iC, &mp); // Investment costs
mv.logsumK=f_lnsum(2, mp.eta, 0, -mv.kv); // Update mv.kv using investments costs, K(c)
// precompute h(c1,c2,c) first element of H(c1,c2,c);
if (iC==0) for (i=0;i<nC*nC;i++) {mv.h1[i]=0;mv.h2[i]=0; hc1[i]=0;hc2[i]=0;}
else {
// omp_set_num_threads(NUM_THREADS);
// #pragma omp parallel shared(mv, g, mp,iC, nC) private(ic1, ic2, neqb, i, j)
{
// printf("There are %d threads\n",omp_get_num_threads());
// #pragma omp for
for (ic1=iC;ic1<nC;ic1++) {
for (ic2=iC;ic2<nC;ic2++) {
j=(ic1-iC)*(nC-iC)+(ic2-iC); // index used for storage in h
mv.h1[j]=0;
mv.h2[j]=0;
hc1[j]=0;
hc2[j]=0;
for (jC=1;jC<=iC;jC++) {
jp=(iC-jC)*nC+iC;
if (mp.pti[jp]>0) {
neqb=(int)g[iC-jC].neqb[id(nC,ic1,ic2,iC-jC,0)];
i=id(nC, ic1, ic2, iC-jC, f_ers(&mp, iC-jC, ic1, ic2, neqb,eqstring)); // index for selected equilibrium
mv.h1[j]=mv.h1[j]+mp.pti[jp]*f_lnsum(nF, mp.eta, g[iC-jC].v10[i], g[iC-jC].v11[i]);
mv.h2[j]=mv.h2[j]+mp.pti[jp]*f_lnsum(nF, mp.eta, g[iC-jC].v20[i], g[iC-jC].v21[i]);
hc1[j]=hc1[j]+mp.pti[jp]*(g[iC-jC].p1[i]*g[iC-jC].ecv11[i]+(1-g[iC-jC].p1[i])*g[iC-jC].ecv10[i]);
hc2[j]=hc2[j]+mp.pti[jp]*(g[iC-jC].p2[i]*g[iC-jC].ecv21[i]+(1-g[iC-jC].p2[i])*g[iC-jC].ecv20[i]);
// printf("f_ers(&mp, iC-jC=%d, ic1=%d, ic2=%d, neqb=%d,eqstring)=%d\n",iC-jC, ic1, ic2, neqb, f_ers(&mp, iC-jC, ic1, ic2, neqb,eqstring));
}
}
}
}
// printf("iC=%d mv.h\n",iC);
// for (ic1=iC;ic1<nC;ic1++) {
// for (ic2=iC;ic2<nC;ic2++) {
// printf("h1[ih(%d,%d,%d)=%d]=%1.5f - h2[ih(%d,%d,%d)=%d]=%1.5f = %1.10f\n",
// ic1,ic2,iC,ih(nC,ic1,ic2,iC),mv.h1[ih(nC,ic1,ic2,iC)],
// ic2,ic1,iC,ih(nC,ic2,ic1,iC),mv.h2[ih(nC,ic2,ic1,iC)],
// mv.h1[ih(nC,ic1,ic2,iC)]-mv.h2[ih(nC,ic2,ic1,iC)]);
// }
// }
// printf("iC=%d hc\n",iC);
// for (ic1=iC;ic1<nC;ic1++) {
// for (ic2=iC;ic2<nC;ic2++) {
// printf("hc1[ih(%d,%d,%d)=%d]=%1.5f - hc2[ih(%d,%d,%d)=%d]=%1.5f = %1.10f\n",
// ic1,ic2,iC,ih(nC,ic1,ic2,iC),hc1[ih(nC,ic1,ic2,iC)],
// ic2,ic1,iC,ih(nC,ic2,ic1,iC),hc2[ih(nC,ic2,ic1,iC)],
// hc1[ih(nC,ic1,ic2,iC)]-hc2[ih(nC,ic2,ic1,iC)]);
// }
// }
}
}
/********************************************************/
// SECTION 3.0: Solve the (c,c,c) corner game
/********************************************************/
ic1=iC; ic2=iC; ieqb=0; // Start c=c1=c2=0, only one equilibrium in the corner endgame
g[iC].pf1[IdOUT]=bne.pf1[IdBNE];
g[iC].pf2[IdOUT]=bne.pf2[IdBNE];
g[iC].ic1[IdOUT]=ic1;
g[iC].ic2[IdOUT]=ic2;
g[iC].ieqb[IdOUT]=ieqb;
g[iC].neqb[IdOUT]=1;
g[iC].c1[IdOUT]=mp.cgrid[ic1];
g[iC].c2[IdOUT]=mp.cgrid[ic2];
g[iC].eqbtype[IdOUT]=1; // 0 = pure strategy equilibrium
// Solve (c,c,c) endgame for firm 1
g[iC].v10[IdOUT]=(bne.pf1[IdBNE]+mp.df*mv.pc*mv.h1[ih(nC, iC, iC, iC)]+mp.df*(1-mv.pc)*mv.logsumK)/(1-mp.df*(1-mv.pc));
// Solve (c,c,c) endgame for firm 2
g[iC].v20[IdOUT]=(bne.pf2[IdBNE]+mp.df*mv.pc*mv.h2[ih(nC, iC, iC, iC)]+mp.df*(1-mv.pc)*mv.logsumK)/(1-mp.df*(1-mv.pc));
g[iC].v11[IdOUT]=g[iC].v10[IdOUT]-mv.kv;
g[iC].v21[IdOUT]=g[iC].v20[IdOUT]-mv.kv;
g[iC].p1[IdOUT]=f_logit(nF, mp.eta, NULL, g[iC].v11[IdOUT], g[iC].v10[IdOUT]);
g[iC].p2[IdOUT]=f_logit(nF, mp.eta, NULL, g[iC].v21[IdOUT], g[iC].v20[IdOUT]);
g[iC].seleqb[id(nC,ic1,ic2,iC,ieqb)]=1;
// Expected costs, (c,c,c) corner game
logsum1=f_lnsum(2, mp.eta, g[iC].v10[IdOUT], g[iC].v11[IdOUT]);
logsum2=f_lnsum(2, mp.eta, g[iC].v20[IdOUT], g[iC].v21[IdOUT]);
EP11 = mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v11[IdOUT])+mv.kv
+mp.df*mv.pc*hc1[ih(nC, iC, iC, iC)];
EP10 = mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v10[IdOUT])
+mp.df*mv.pc*hc1[ih(nC, iC, iC, iC)];
EP21 = mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v21[IdOUT])+mv.kv
+mp.df*mv.pc*hc2[ih(nC, iC, iC, iC)];
EP20 = mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v20[IdOUT])
+mp.df*mv.pc*hc2[ih(nC, iC, iC, iC)];
p1=g[iC].p1[IdOUT];
p2=g[iC].p2[IdOUT];
//firm 1 symbolic solution
j=ih(nC, ic1, ic2, iC);
B=mp.df*(1-mv.pc); //used everywhere below!!!!
AI1=mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v11[IdOUT])+mv.kv
+mp.df*mv.pc*hc1[j];
AN1=mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v10[IdOUT])
+mp.df*mv.pc*hc1[j];
g[iC].ecv10[IdOUT]=-(AN1 + AI1*B*p1 - AN1*B*p1)/(B - 1);//CN1_ccc
g[iC].ecv11[IdOUT]=-(AI1 - AI1*B + AN1*B + AI1*B*p1 - AN1*B*p1)/(B - 1);//CI1_ccc
//firm 1 analytic solution
// g[iC].ecv11[IdOUT]=(EP11+((mp.df*(1-mv.pc)*(1-p1))/(1-(1-p1)*mp.df*(1-mv.pc)))*EP10)/(1-(mp.df*(1-mv.pc)*p1+((mp.df*(1-mv.pc)*(1-p1)*mp.df*(1-mv.pc)*p1)/(1-(1-p1)*mp.df*(1-mv.pc)))));
// g[iC].ecv10[IdOUT]=(EP10+mp.df*(1-mv.pc)*p1*g[iC].ecv11[IdOUT])/(1-(1-p1)*mp.df*(1-mv.pc));
//firm 2 symbolic solution
AI2=mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v21[IdOUT])+mv.kv
+mp.df*mv.pc*hc2[j];
AN2=mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v20[IdOUT])
+mp.df*mv.pc*hc2[j];
// CN2_ccc =
// -(AN2 + AI2*B*p2 - AN2*B*p2)/(B - 1)
// CI2_ccc =
// -(AI2 - AI2*B + AN2*B + AI2*B*p2 - AN2*B*p2)/(B - 1)
//firm 2 analytic solution
g[iC].ecv21[IdOUT]=(EP21+((mp.df*(1-mv.pc)*(1-p2))/(1-(1-p2)*mp.df*(1-mv.pc)))*EP20)/(1-(mp.df*(1-mv.pc)*p2+((mp.df*(1-mv.pc)*(1-p2)*mp.df*(1-mv.pc)*p2)/(1-(1-p2)*mp.df*(1-mv.pc)))));
g[iC].ecv20[IdOUT]=(EP20+mp.df*(1-mv.pc)*p2*g[iC].ecv21[IdOUT])/(1-(1-p2)*mp.df*(1-mv.pc));
/**************************************************************************/
// SECTION 3.1: solve the (c1,c,c) edge game
/**************************************************************************/
ic2=iC; ieqb=0; //only one equilibrium in the edge endgame
for (ic1=iC+1;ic1<nC;ic1++) {
if (((ic1z==ic1) && (ic2z==iC)) || (iC>iCz) || (iCz==0)) {
// Solve for BN-equaliprium prices and profits
// Part of formula ??
// Save output
g[iC].pf1[IdOUT]=bne.pf1[IdBNE];
g[iC].pf2[IdOUT]=bne.pf2[IdBNE];
g[iC].ic1[IdOUT]=ic1;
g[iC].ic2[IdOUT]=ic2;
g[iC].ieqb[IdOUT]=ieqb;
g[iC].neqb[IdOUT]=1;
g[iC].c1[IdOUT]=mp.cgrid[ic1];
g[iC].c2[IdOUT]=mp.cgrid[ic2];
g[iC].eqbtype[IdOUT]=1;
g[iC].seleqb[IdOUT]=1;
// solve value functions for firm 1
q=mv.pc*mv.h1[ih(nC, iC, iC, iC)]+(1-mv.pc)*g[iC].v10[id(nC, iC, iC, iC, 0)];
g[iC].v11[IdOUT]=bne.pf1[IdBNE]-mv.kv+mp.df*q+mp.df*(1-mv.pc)*mv.logsumK;
g[iC].v10[IdOUT]=f_solvevf(
bne.pf1[IdBNE]+mp.df*mv.pc*mv.h1[ih(nC, ic1, iC, iC)],
(1-mv.pc)*mp.df,
g[iC].v11[id(nC, ic1, iC, iC, 0)],
mp.eta, &mp);
g[iC].p1[IdOUT]=f_logit(nF, mp.eta, NULL, g[iC].v11[IdOUT], g[iC].v10[IdOUT]);
// solve value functions for firm 2
q=mv.pc*mv.h2[ih(nC, iC, iC, iC)]+(1-mv.pc)*g[iC].v20[id(nC, iC, iC, iC, 0)];
g[iC].v20[IdOUT]=(bne.pf2[IdBNE]
+mp.df*g[iC].p1[IdOUT]*q
+mp.df*(1-g[iC].p1[IdOUT])*mv.pc*mv.h2[ih(nC, ic1, iC, iC)]
+mp.df*(1-mv.pc)*mv.logsumK
)/(1-(1-mv.pc)*mp.df*(1-g[iC].p1[IdOUT])); // equation (26)
g[iC].v21[IdOUT]=g[iC].v20[IdOUT]-mv.kv;
g[iC].p2[IdOUT]=f_logit(nF, mp.eta, NULL, -mv.kv, 0);
// Expected costs
logsum1=f_lnsum(2, mp.eta, g[iC].v10[IdOUT], g[iC].v11[IdOUT]);
logsum2=f_lnsum(2, mp.eta, g[iC].v20[IdOUT], g[iC].v21[IdOUT]);
EP11 = mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v11[IdOUT])+mv.kv
+mp.df*mv.pc*(hc1[ih(nC, iC, iC, iC)]);
EP10 = mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v10[IdOUT])
+mp.df*mv.pc*(hc1[ih(nC, ic1, iC, iC)]);
EP21 = mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v21[IdOUT])+mv.kv
+mp.df*mv.pc*(g[iC].p1[IdOUT]*hc2[ih(nC, iC, iC, iC)]+(1-g[iC].p1[IdOUT])*hc2[ih(nC, ic1, iC, iC)]);
EP20 = mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v20[IdOUT])
+mp.df*mv.pc*(g[iC].p1[IdOUT]*hc2[ih(nC, iC, iC, iC)]+(1-g[iC].p1[IdOUT])*hc2[ih(nC, ic1, iC, iC)]);
iccc=id(nC, iC, iC, iC, 0);
//firm1 symbolic solution
j=ih(nC, ic1, ic2, iC); //index of current state point (without ieqb)
p1=g[iC].p1[IdOUT];
p2=g[iC].p2[IdOUT];
AN1=mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v10[IdOUT])
+mp.df*mv.pc*hc1[j];
g[iC].ecv11[IdOUT] =mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v11[IdOUT])+mv.kv
+mp.df*mv.pc*(hc1[ih(nC, iC, iC, iC)])
+B*(g[iC].p1[iccc]*g[iC].ecv11[iccc] +(1-g[iC].p1[iccc])*g[iC].ecv10[iccc]); //CI1_c1cc
g[iC].ecv10[IdOUT] =(AN1 + g[iC].ecv11[IdOUT]*B*p1)/(B*p1 - B + 1); //CN1_c1cc
//firm1 analytic solution
// g[iC].ecv11[IdOUT] =EP11 +mp.df*(1-mv.pc)*( g[iC].p1[iccc])*g[iC].ecv11[iccc]
// +mp.df*(1-mv.pc)*(1-g[iC].p1[iccc])*g[iC].ecv10[iccc];
// g[iC].ecv10[IdOUT] =(EP10 + mp.df*(1-mv.pc)*g[iC].p1[IdOUT]*g[iC].ecv11[IdOUT])
// /(1-mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT]));
//firm 2 analytic solution
f1=(mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT])*g[iC].p2[IdOUT])/(1-mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT])*g[iC].p2[IdOUT]);
g[iC].ecv20[IdOUT]=(EP20+f1*EP20+(mp.df*(1-mv.pc)*g[iC].p1[IdOUT]+f1)*g[iC].p2[iccc]*g[iC].ecv21[iccc]+f1*(mp.df*(1-mv.pc)*g[iC].p1[IdOUT]*(1-g[iC].p2[iccc])*g[iC].ecv20[iccc]))
/(1-(1+f1)*mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT])*(1-g[iC].p2[IdOUT]));
g[iC].ecv21[IdOUT]=(EP21+g[iC].p2[IdOUT]*g[iC].ecv21[iccc]+mp.df*(1-mv.pc)*g[iC].p1[IdOUT]*(1-g[iC].p2[IdOUT])*g[iC].ecv20[iccc]+mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT])*(1-g[iC].p2[IdOUT])*g[iC].ecv20[IdOUT])
/(1-mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT])*g[iC].p2[IdOUT]);
}
}
/**************************************************************************/
// SECTION 3.2: solve the (c,c2,c) edge game
/**************************************************************************/
ic1=iC; ieqb=0; //only one equilibrium in the edge endgame
for (ic2=iC+1;ic2<nC;ic2++) {
if (((ic2z==ic2) && (ic1z==iC)) || (iC>iCz) || (iCz==0)) {
// Save output
g[iC].pf1[IdOUT]=bne.pf1[IdBNE];
g[iC].pf2[IdOUT]=bne.pf2[IdBNE];
g[iC].ic1[IdOUT]=ic1;
g[iC].ic2[IdOUT]=ic2;
g[iC].ieqb[IdOUT]=ieqb;
g[iC].neqb[IdOUT]=1;
g[iC].c1[IdOUT]=mp.cgrid[ic1];
g[iC].c2[IdOUT]=mp.cgrid[ic2];
g[iC].eqbtype[IdOUT]=1;
g[iC].seleqb[IdOUT]=1;
// solve value functions for firm 2
q=mv.pc*mv.h2[ih(nC, iC, iC, iC)]+(1-mv.pc)*g[iC].v20[id(nC, iC, iC, iC, 0)];
g[iC].v21[IdOUT]=bne.pf2[IdBNE]-mv.kv+mp.df*q+mp.df*(1-mv.pc)*mv.logsumK;
g[iC].v20[IdOUT]=f_solvevf(
bne.pf2[IdBNE]+mp.df*mv.pc*mv.h2[ih(nC, iC, ic2, iC)],
(1-mv.pc)*mp.df,
g[iC].v21[IdOUT],
mp.eta, &mp);
g[iC].p2[IdOUT]=f_logit(nF, mp.eta, NULL, g[iC].v21[IdOUT], g[iC].v20[IdOUT]);
// solve value functions for firm 1
q=mv.pc*mv.h1[ih(nC, iC, iC, iC)]+(1-mv.pc)*g[iC].v10[id(nC, iC, iC, iC, 0)];
g[iC].v10[IdOUT]=(
bne.pf1[IdBNE]
+mp.df*g[iC].p2[id(nC,iC,ic2,iC,0)]*q
+mp.df*(1-g[iC].p2[id(nC,iC,ic2,iC,0)])*mv.pc*mv.h1[ih(nC, iC, ic2, iC)]
+mp.df*(1-mv.pc)*mv.logsumK
)/(1-(1-mv.pc)*mp.df*(1-g[iC].p2[id(nC,iC,ic2,iC,0)])); // equation (26)
g[iC].v11[IdOUT]=g[iC].v10[IdOUT]-mv.kv;
g[iC].p1[IdOUT]=f_logit(nF, mp.eta, NULL, g[iC].v11[IdOUT], g[iC].v10[IdOUT]);
// Expected costs
logsum1=f_lnsum(2, mp.eta, g[iC].v10[IdOUT], g[iC].v11[IdOUT]);
logsum2=f_lnsum(2, mp.eta, g[iC].v20[IdOUT], g[iC].v21[IdOUT]);
EP11 = mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v11[IdOUT])+mv.kv
+mp.df*mv.pc*(g[iC].p2[IdOUT]*hc1[ih(nC, iC, iC, iC)]+(1-g[iC].p2[IdOUT])*hc1[ih(nC, iC, ic2, iC)]);
EP10 = mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v10[IdOUT])
+mp.df*mv.pc*(g[iC].p2[IdOUT]*hc1[ih(nC, iC, iC, iC)]+(1-g[iC].p2[IdOUT])*hc1[ih(nC, iC, ic2, iC)]);
EP21 = mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v21[IdOUT])+mv.kv
+mp.df*mv.pc*(hc2[ih(nC, iC, iC, iC)]);
EP20 = mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v20[IdOUT])
+mp.df*mv.pc*(hc2[ih(nC, iC, ic2, iC)]);
iccc=id(nC, iC, iC, iC, 0);
//firm1 symbolic solution
j=ih(nC, ic1, ic2, iC); //index of current state point (without ieqb)
p1=g[iC].p1[IdOUT];
p2=g[iC].p2[IdOUT];
AN1=mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v10[IdOUT])
+mp.df*mv.pc*(g[iC].p2[IdOUT]*hc1[ih(nC,iC,iC,iC)]+(1-g[iC].p2[IdOUT])*hc1[j])
+B*p2*(g[iC].p1[iccc]*g[iC].ecv11[iccc]+(1-g[iC].p1[iccc])*g[iC].ecv10[iccc]);
AI1=mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v11[IdOUT])+mv.kv
+mp.df*mv.pc*(g[iC].p2[IdOUT]*hc1[ih(nC,iC,iC,iC)]+(1-g[iC].p2[IdOUT])*hc1[j])
+ B*p2*(g[iC].p1[iccc]*g[iC].ecv11[iccc]+(1-g[iC].p1[iccc])*g[iC].ecv10[iccc]);
g[iC].ecv10[IdOUT]=(AN1 + AI1*B*p1 - AN1*B*p1 - AI1*B*p1*p2 + AN1*B*p1*p2)/(B*p2 - B + 1);//CN1_cc2c
g[iC].ecv11[IdOUT]=(AI1 - AI1*B + AN1*B + AI1*B*p1 + AI1*B*p2 - AN1*B*p1 - AN1*B*p2 - AI1*B*p1*p2 + AN1*B*p1*p2)/(B*p2 - B + 1);//CI1_cc2c
//firm1 analytic solution
// f1=(mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT])*g[iC].p1[IdOUT])/(1-mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT])*g[iC].p1[IdOUT]);
// g[iC].ecv10[IdOUT]=(EP10+f1*EP10+(mp.df*(1-mv.pc)*g[iC].p2[IdOUT]+f1)*g[iC].p1[iccc]*g[iC].ecv11[iccc]+f1*(mp.df*(1-mv.pc)*g[iC].p2[IdOUT]*(1-g[iC].p1[iccc])*g[iC].ecv10[iccc]))
// /(1-(1+f1)*mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT])*(1-g[iC].p1[IdOUT]));
// g[iC].ecv11[IdOUT]=(EP11+g[iC].p1[IdOUT]*g[iC].ecv11[iccc]+mp.df*(1-mv.pc)*g[iC].p2[IdOUT]*(1-g[iC].p1[IdOUT])*g[iC].ecv10[iccc]+mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT])*(1-g[iC].p1[IdOUT])*g[iC].ecv10[IdOUT])
// /(1-mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT])*g[iC].p1[IdOUT]);
//firm 2 analytic solution
g[iC].ecv21[IdOUT] =EP21 +mp.df*(1-mv.pc)*( g[iC].p2[iccc])*g[iC].ecv21[iccc]
+mp.df*(1-mv.pc)*(1-g[iC].p2[iccc])*g[iC].ecv20[iccc];
g[iC].ecv20[IdOUT] =(EP20 + mp.df*(1-mv.pc)*g[iC].p2[IdOUT]*g[iC].ecv21[IdOUT])
/(1-mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT]));
}
}
/**************************************************************************/
// SECTION 3.3: solve the (c1,c2,c) interior game
/**************************************************************************/
// omp_set_num_threads(NUM_THREADS);
// #pragma omp parallel shared(mv, g, mp, nC, iC, bne) private(ic1, ic2, i1, i2, A0, A1, B1, C0, C1, a0, a1, a2, pstar, nroot, ieqb, i, j, A, B, v0_0, v0_1, pbr, save, neqb, nmeqb)
// {
// // printf("There are %d threads\n",omp_get_num_threads());
// #pragma omp for
//loop over the interier points
for (ic1=iC+1;ic1<nC;ic1++) {
for (ic2=iC+1;ic2<nC;ic2++) {
if (((ic1z==ic1) && (ic2z==ic2)) || (iC>iCz) || (iCz==0)) {
j=(ic1-iC)*(nC-iC)+(ic2-iC); // index used for storage in h
i1=id(nC, ic1, iC, iC, 0); //c1 c c
i2=id(nC, iC, ic2, iC, 0); //c c2 c
// populate brc sturcture
brc.pc=mv.pc; // XXX appears in two structures
brc.kv=mv.kv; // XXX appears in two structures
brc.pf[0]=bne.pf1[IdBNE];
brc.pf[1]=bne.pf2[IdBNE];
brc.x0[0]= mp.df*(brc.pc*mv.h1[ih(nC,iC,iC,iC)] + (1-brc.pc)*g[iC].v10[id(nC,iC,iC,iC,0)]);
brc.x1[0]= mp.df*(brc.pc*mv.h1[ih(nC,iC,ic2,iC)] + (1-brc.pc)*g[iC].v10[id(nC,iC,ic2,iC,0)]);
brc.x0[1]= mp.df*(brc.pc*mv.h2[ih(nC,iC,iC,iC)] + (1-brc.pc)*g[iC].v20[id(nC,iC,iC,iC,0)]);
brc.x1[1]= mp.df*(brc.pc*mv.h2[ih(nC,ic1,iC,iC)] + (1-brc.pc)*g[iC].v20[id(nC,ic1,iC,iC,0)]);
brc.A0[0]= bne.pf1[IdBNE]+mp.df*mv.pc*mv.h1[ih(nC, iC, iC, iC)]+(1-mv.pc)*f_lnsum(nF, mp.eta, g[iC].v10[i1], g[iC].v11[i1]);
brc.A1[0]= mp.df*mv.pc*mv.h1[ih(nC,ic1,ic2,iC)];
brc.A0[1]= bne.pf2[IdBNE]+mp.df*mv.pc*mv.h2[ih(nC, iC, iC, iC)]+(1-mv.pc)*f_lnsum(nF, mp.eta, g[iC].v20[i2], g[iC].v21[i2]);
brc.A1[1]= mp.df*mv.pc*mv.h2[ih(nC,ic1,ic2,iC)];
brc.B[1]=mp.df*(1-brc.pc);
brc.B[0]=mp.df*(1-brc.pc);
//initialize the number of equilibria to be stored in the g structure
g[iC].neqb[id(nC,ic1,ic2,iC,0)]=0;
//find equilibria
if ((mp.eta>0) && (mp.analytical==false)){
s_ffxp((f_br2p1_sm), &mp, &brc, &g[iC], ic1, ic2, iC, nC);
// s_ffxp((f_br1p2_sm), &mp, &brc, &g[iC], ic1, ic2, iC, nC);
}
else {
analytical_solutions (ic1,ic2,iC,mp,mv,bne,g,br,eqstring);
}
//number of equilibria found
//neqb=f_neqb(nC, ic1, ic2, iC, g); XXXX
neqb=(int)g[iC].neqb[id(nC,ic1,ic2,iC,0)];
#ifdef PRINTnrstagempe
if (neqb==PRINTnrstagempe) {
neqstr=nC*(nC+1)*(2*nC+1)/6;
printf("%d stage MPE: iC=%d, ic1=%d, ic2=%d ESS= ",PRINTnrstagempe,iC+1,ic1+1,ic2+1);
printeqb(eqstring,neqstr,lexindex1(eqstring,neqstr),NULL);
};
#endif
// Save indices and costs (remaining elements of g are stored inside f_br2p1_am
for (ieqb=0;ieqb<neqb;ieqb++) {
g[iC].ic1[IdOUT]=ic1; //0
g[iC].ic2[IdOUT]=ic2; //1
g[iC].ieqb[IdOUT]=ieqb; //2
g[iC].c1[IdOUT]=mp.cgrid[ic1]; //3
g[iC].c2[IdOUT]=mp.cgrid[ic2]; //4
// 5-11: eqbtype, v10,v11,b20, v21, p1, p2: stored inside f_br2p1_am
g[iC].seleqb[id(nC,ic1,ic2,iC,ieqb)]=(ieqb==f_ers(&mp, iC, ic1, ic2, neqb,eqstring)?1.0:0.0); //12
g[iC].pf1[IdOUT]=bne.pf1[IdBNE]; //13
g[iC].pf2[IdOUT]=bne.pf2[IdBNE]; //14
//calculate analytical solutions and save to proper output structures
// Expected costs
logsum1=f_lnsum(2, mp.eta, g[iC].v10[IdOUT], g[iC].v11[IdOUT]);
logsum2=f_lnsum(2, mp.eta, g[iC].v20[IdOUT], g[iC].v21[IdOUT]);
EP11 = mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v11[IdOUT])+mv.kv
+mp.df*mv.pc*(g[iC].p2[IdOUT]*hc1[ih(nC, iC , iC, iC)]+(1-g[iC].p2[IdOUT])*hc1[ih(nC, iC , ic2, iC)]); ///BUG HERE
// +mp.df*mv.pc*(g[iC].p2[IdOUT]*hc1[ih(nC, ic1, iC, iC)]+(1-g[iC].p2[IdOUT])*hc1[ih(nC, ic1, ic2, iC)]); ///BUG HERE
EP21 = mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v21[IdOUT])+mv.kv
+mp.df*mv.pc*(g[iC].p1[IdOUT]*hc2[ih(nC, iC, iC, iC)]+(1-g[iC].p1[IdOUT])*hc2[ih(nC, ic1, iC, iC)]);
// +mp.df*mv.pc*(g[iC].p1[IdOUT]*hc2[ih(nC, iC, ic2, iC)]+(1-g[iC].p1[IdOUT])*hc2[ih(nC, ic1, ic2, iC)]); ///BUG HERE
EP10 = mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v10[IdOUT])
+mp.df*mv.pc*(g[iC].p2[IdOUT]*hc1[ih(nC, ic1, iC, iC)]+(1-g[iC].p2[IdOUT])*hc1[ih(nC, ic1, ic2, iC)]);
EP20 = mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v20[IdOUT])
+mp.df*mv.pc*(g[iC].p1[IdOUT]*hc2[ih(nC, iC, ic2, iC)]+(1-g[iC].p1[IdOUT])*hc2[ih(nC, ic1, ic2, iC)]);
iccc=id(nC, iC, iC, iC, 0); //0 for first and only equilibrium at corners and edges
i1=id(nC, ic1, iC, iC, 0);
i2=id(nC, iC, ic2, iC, 0);
//firm1 symbolic solution
j=ih(nC, ic1, ic2, iC); //index of current state point (without ieqb)
p1=g[iC].p1[IdOUT];
p2=g[iC].p2[IdOUT];
g[iC].ecv11[IdOUT]=mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v11[IdOUT])+mv.kv
+mp.df*mv.pc*(p2 *hc1[ih(nC, iC, iC, iC)]
+(1-p2)*hc1[ih(nC, iC, ic2, iC)])
+B*p2* (g[iC].p1[iccc]*g[iC].ecv11[iccc]+(1-g[iC].p1[iccc])*g[iC].ecv10[iccc])
+B*(1-p2)*(g[iC].p1[i2] *g[iC].ecv11[i2] +(1-g[iC].p1[i2]) *g[iC].ecv10[i2]); //CI1_c1c2c
AN1= mp.dt*bne.s1[IdBNE]*mp.cgrid[ic1]-mp.eta*(EULER+logsum1-g[iC].v10[IdOUT])
+mp.df*mv.pc*(p2*hc1[ih(nC, ic1, iC, iC)]+(1-p2)*hc1[j])
+B*p2*(g[iC].p1[i1]*g[iC].ecv11[i1]+(1-g[iC].p1[i1])*g[iC].ecv10[i1]);
g[iC].ecv10[IdOUT]=(AN1 + g[iC].ecv11[IdOUT]*B*p1 - g[iC].ecv11[IdOUT]*B*p1*p2)/(B*p1 - B + B*p2 - B*p1*p2 + 1);//CN1_c1c2c
//firm1 analytic solution
// g[iC].ecv11[IdOUT]=EP11 + mp.df*(1-mv.pc)*g[iC].p2[IdOUT] *(g[iC].p1[iccc]*g[iC].ecv11[iccc]+(1-g[iC].p1[iccc])*g[iC].ecv10[iccc])
// + mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT]) *(g[iC].p1[i2]*g[iC].ecv11[i2] +(1-g[iC].p1[i2]) *g[iC].ecv10[i2]);
// g[iC].ecv10[IdOUT]=(EP10+mp.df*(1-mv.pc)* g[iC].p2[IdOUT] *(g[iC].p1[i1]* g[iC].ecv11[i1]
// +(1-g[iC].p1[i1])*g[iC].ecv10[i1])
// +mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT]) *g[iC].p1[IdOUT]*g[iC].ecv11[IdOUT])
// /(1-mp.df*(1-mv.pc)*(1-g[iC].p2[IdOUT])*(1-g[iC].p1[IdOUT]));
//firm2 symbolic solution
// g[iC].ecv21[IdOUT]=mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v21[IdOUT])+mv.kv
// +mp.df*mv.pc*(p1*hc2[ih(nC, iC, iC, iC)]+(1-p1)*hc2[ih(nC, ic1, iC, iC)])
// +B*p1 *(g[iC].p2[iccc]*g[iC].ecv21[iccc]+(1-g[iC].p2[iccc])*g[iC].ecv20[iccc])
// +B*(1-p1)*(g[iC].p2[i1]*g[iC].ecv21[i1] +(1-g[iC].p2[i1]) *g[iC].ecv20[i1]);//CI2_c1c2c
// AN2= mp.dt*bne.s2[IdBNE]*mp.cgrid[ic2]-mp.eta*(EULER+logsum2-g[iC].v20[IdOUT])
// +mp.df*mv.pc*(p1*hc2[ih(nC, iC, ic2, iC)]+(1-p1)*hc2[j])
// +B*p1*(g[iC].p2[i2]*g[iC].ecv21[i2]+(1-g[iC].p2[i2])*g[iC].ecv20[i2]);
// g[iC].ecv20[IdOUT]=(AN2 + g[iC].ecv21[IdOUT]*B*p2 - g[iC].ecv21[IdOUT]*B*p1*p2)/(B*p1 - B + B*p2 - B*p1*p2 + 1);//CN2_c1c2c
//firm2 analytic solution
g[iC].ecv21[IdOUT]=EP21 + mp.df*(1-mv.pc)*g[iC].p1[IdOUT] *(g[iC].p2[iccc]*g[iC].ecv21[iccc]+(1-g[iC].p2[iccc])*g[iC].ecv20[iccc])
+ mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT]) *(g[iC].p2[i1]*g[iC].ecv21[i1] +(1-g[iC].p2[i1]) *g[iC].ecv20[i1]);
g[iC].ecv20[IdOUT]=(EP20+mp.df*(1-mv.pc)*g[iC].p1[IdOUT] *(g[iC].p2[i2]*g[iC].ecv21[i2]+(1-g[iC].p2[i2])*g[iC].ecv20[i2])
+mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT])*g[iC].p2[IdOUT]*g[iC].ecv21[IdOUT] )
/(1-mp.df*(1-mv.pc)*(1-g[iC].p1[IdOUT])*(1-g[iC].p2[IdOUT]));
}
// g[iC].ecv10[IdOUT]=(EP10+f1*EP10+(mp.df*g[iC].p2[IdOUT]+f1)*g[iC].p1[iccc]*g[iC].ecv11[iccc]+f1*(mp.df*g[iC].p2[IdOUT]*(1-g[iC].p1[iccc])*g[iC].ecv10[iccc]))
// /(1-(1+f1)*mp.df*(1-g[iC].p2[IdOUT])*(1-g[iC].p1[IdOUT]));
}
}
}
// } // end parallel execution
//compute totals for the whole layer
ieqb=0; //only one equilibrium in the edge endgame
for (ic1=iC;ic1<nC;ic1++) {
for (ic2=iC;ic2<nC;ic2++) {
if (((ic1z==ic1) && (ic2z==ic2)) || (iC>iCz) || (iCz==0)) {
if (ic1>iC && ic2>iC) neqb=(int)g[iC].neqb[id(nC,ic1,ic2,iC,0)]; //interior
else neqb=1; //corner and edges
for (ieqb=0;ieqb<neqb;ieqb++) {
//social surplus = total revenue - total cost (conditional on who has the right of move)
g[iC].ecm1[IdOUT]=mp.dt*MAX(mp.cgrid[ic1],mp.cgrid[ic2])/(1-mp.df) - (g[iC].p1[IdOUT]*g[iC].ecv11[IdOUT] + (1-g[iC].p1[IdOUT])*g[iC].ecv10[IdOUT]
+g[iC].p2[IdOUT]*g[iC].ecv21[IdOUT] + (1-g[iC].p2[IdOUT])*g[iC].ecv20[IdOUT]);
//printf("neqb=%d, ieqb=%d, p1=%1.4f, ecv11=%1.4f, ecv10=%1.4f, ecm1=%1.4f, ecm2=%1.4f\n",neqb ,ieqb, g[iC].p1[IdOUT], g[iC].ecv11[IdOUT], g[iC].ecv10[IdOUT],g[iC].ecm1[IdOUT],g[iC].ecm2[IdOUT] );
}
}
}
}
} //continue loop over iC
free(mv.h1);
free(mv.h2);
free(hc1);
free(hc2);
free(mv.eqbinfo);
//printf("Run %d\n",COUNT++);
}