void gensf(void)
{
int pl, i, j;
Outcome z;
allocsf();
behavtorealprob(0); /* get realization probabilities of leaves */
/* sf payoff matrices */
for (z=outcomes; z < lastoutcome; z++)
{
Node u = z->whichnode;
i = u->defseq[1] - firstmove[1];
j = u->defseq[2] - firstmove[2];
for (pl=1; pl < PLAYERS; pl++)
sfpay[i][j][pl-1] = ratadd(sfpay[i][j][pl-1],
ratmult(u->defseq[0]->realprob, z->pay[pl-1]) );
}
/* sf constraint matrices, sparse fill */
for (pl=1; pl < PLAYERS; pl++)
{
sfconstr[pl][0][0] = 1; /* empty sequence */
for (i=0; i < nisets[pl]; i++)
sfconstr[pl][i+1][(firstiset[pl]+i)->seqin - firstmove[pl]] = -1;
for (j=1; j < nseqs[pl]; j++)
sfconstr[pl][(firstmove[pl]+j)->atiset - firstiset[pl]+1][j] = 1;
}
} /* end of gensf() */
void behavtomixed(int pl)
{
Rat r;
int i, strat;
for (strat = 0; strat < nstrats[pl]; strat++)
{
strattomovetuple(strat, pl);
/* multiply behavior probabilities */
r = ratfromi(1);
for (i=0; i<nisets[pl]; i++)
if(movetuple[pl][i])
r = ratmult(r, movetuple[pl][i]->behavprob) ;
/* check if mixed strat probabilities themselves
* troublesome. Does not seem so.
* ...........comment out code..........
{
char s[MAXSTRL];
r = ratmult(r, movetuple[pl][i]->behavprob) ;
rattoa(r, s);
printf("Debug: mixed prob %2d is %s\n", i, s) ;
}
*/
mixedstrat[pl][strat] = r;
}
} /* end of behavtomixed(pl) */
void gennf(void)
{
int pl, i, j;
int *slist[PLAYERS]; /* list of strategies for nf generation */
int nl[PLAYERS]; /* no of strategies compatible with leave seq */
Outcome z;
Payvec v;
Payvec *nfrow;
int nfcolpos;
/* determine nf size and allocate */
for (pl=0; pl < PLAYERS; pl++)
nstrats[pl] = numstratsnfpre(pl);
allocnf();
for (pl=0; pl < PLAYERS; pl++)
slist[pl] = TALLOC (nstrats[pl], int);
behavtorealprob(0); /* get realization probabilities of leaves */
/* nf payoff matrices */
for (z=outcomes; z < lastoutcome; z++)
{
Node u = z->whichnode;
for (pl=1; pl < PLAYERS; pl++)
{
v[pl-1] = ratmult(u->defseq[0]->realprob, z->pay[pl-1] );
nl[pl] = seqtostratlist (u->defseq[pl], pl, slist[pl]);
}
for (i=0; i < nl[1]; i++)
{
nfrow = nfpay[slist[1][i]];
for (j=0; j < nl[2]; j++)
{
nfcolpos = slist[2][j];
for (pl=1; pl < PLAYERS; pl++)
nfrow[nfcolpos][pl-1] =
ratadd(nfrow[nfcolpos][pl-1], v[pl-1]);
}
}
} /* end of for all outcomes z */
for (pl=0; pl < PLAYERS; pl++)
free(slist[pl]);
} /* end of gennf() */
/* returns quotient a/b, normalized */
Rat ratdiv (Rat a, Rat b)
{
return ratmult(a, ratinv(b) );
}
void setrsfcomplconstr (int paytopl, Rat ** intoM,
int rowoffset, int coloffset, Bool negpaymatrix,
Rat * rhsvec, Bool negrhs)
{
int othpl = 3 - paytopl; /* other player */
int i,j,k, a;
Rat s;
Rat * tmprow; /* temporary row for triple matrix product comptn */
tmprow = TALLOC( nseqs[othpl] , Rat);
/* first blockrow of dim redsfdim[paytopl] */
for (i = 0; i < redsfdim[paytopl]; i++)
{
/* compute tmprow (with index j ) as
* if paytopl==1: row i of K\T A,
* if paytopl==2: row i of L\T B\T
*/
for (j = 0; j < nseqs[othpl]; j++)
{
s = ratfromi(0);
for (k = 0; k < nseqs[paytopl]; k++)
/* a = entry of K\T resp. L\T */
if ((a = realplfromredsf[paytopl][k][i] ) != 0)
s = ratadd( s, ratmult( ratfromi(a),
(paytopl==1) ? sfpay[k][j][0] : sfpay[j][k][1] )) ;
tmprow[j] = s;
}
/* compute i,k entry of
* if paytopl==1: K\T A L = Ahat
* if paytopl==2: L\T B\T K = Bhat \T
* comments from now only for paytopl==1
*/
for (k = 0; k < redsfdim[othpl]; k++)
{
s = ratfromi(0);
for (j = 0; j < nseqs[othpl]; j++)
if ( (a = realplfromredsf [othpl][j][k] ) != 0)
s = ratadd( s, ratmult( ratfromi(a), tmprow[j] )) ;
/* fill matrix entry with -Ahat */
intoM [ rowoffset + i] [ coloffset + k ] =
negpaymatrix ? ratneg(s) : s ;
}
/* set matrix entry for Ehat\T */
for (j = 0; j < irreddim[paytopl]; j++)
{
s = ratfromi( redsfconstr [paytopl][j][i] );
intoM [ rowoffset + i] [ coloffset + redsfdim[othpl] + j] =
negpaymatrix ? s : ratneg(s) ;
}
/* set LCP rhs entry i of K\T A l = ahat */
s = ratfromi(0);
for (j = 0; j < nseqs[othpl]; j++)
s = ratadd( s, ratmult( tmprow[j],
ratfromi ( realplconst [othpl] [j] ) ) ) ;
rhsvec[i] = negrhs ? ratneg(s) : s ;
}
/* second blockrow of dim irreddim [othpl] */
for (i = 0; i < irreddim [othpl]; i++)
{
/* set LCP matrix entry for -Fhat */
for (j = 0; j < redsfdim[othpl]; j++)
{
s = ratfromi( redsfconstr [othpl][i][j] );
intoM [ rowoffset + redsfdim[paytopl] + i ] [ coloffset + j] =
negpaymatrix ? ratneg(s) : s ;
}
/* set LCP rhs entry i of -fhat */
s = ratfromi( redsfrhs [othpl][i] );
rhsvec[ redsfdim[paytopl] + i] = negrhs ? s : ratneg(s) ;
}
free(tmprow);
}
