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add (M+1)st Price auction global-view script

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Markus Teich 2016-06-10 16:36:22 +02:00
parent d4360a4f8b
commit c75341d052
1 changed files with 16 additions and 17 deletions
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33
gp-scripts/m+1stPrice
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@ -5,6 +5,8 @@
\\ Adapt the following values to your needs
\\\\\\\\\\\\
\\ auction parameter
M = 1
\\ amount of bidders
n = 2^3
\\ amount of possible prices
@ -16,20 +18,18 @@ bid = vector(n,i,random(k)+1)
\\bid = vector(n,i,(i+1)%2) \\ second bidder wins (with ties)
\\ prime finite field setup (result may be ambiguous if your prime is too small, 4*n*k seems to work fine)
q = prime(4*n*k)
\\p = 263
\\q = (p-1)/2
\\ use save prime p
q = prime(2^12)
p = 2*q + 1
\\\\\\\\\\\\
\\ SETUP
\\\\\\\\\\\\
\\ p not needed? wat?
\\p = 47
\\ get generator / primitive element for Z_q
var = 'x \\ copy pasta from internet
pe=ffgen(minpoly(ffprimroot(ffgen(ffinit(q,1))),var),var) \\ get primitive element
1/(fforder(pe) == q-1) \\ error out, if ord(pe) is wrong
g = Mod(eval(Str(pe)), q) \\ dirty hack to convert t_FFELEM to t_INT
\\ get generator / primitive element for G_q
\\var = 'x \\ copy pasta from internet
\\pe=ffgen(minpoly(ffprimroot(ffgen(ffinit(p,1))),var),var) \\ get primitive element
\\1/(fforder(pe) == p-1) \\ error out, if ord(pe) is wrong
\\g = Mod(eval(Str(pe))^2, p) \\ dirty hack to convert t_FFELEM to t_INT
g = Mod(4, p)
\\\\\\\\\\\\
\\ PROLOG
@ -66,8 +66,8 @@ beta = matrix(n,k,i,j, g^r[i,j])
\\ multiplicative shares
\\ first index level = owning agent id (multiplicative share)
\\ second index level = agent id, price id
Gamma = vector(n,a,matrix(n,k,i,j, ( prod(h=1,n,prod(d=j+1,k,alpha[h,d])) * prod(d=1,j-1,alpha[i,d]) * prod(h=1,i-1,alpha[h,j]) )^m[a][i,j] ))
Delta = vector(n,a,matrix(n,k,i,j, ( prod(h=1,n,prod(d=j+1,k, beta[h,d])) * prod(d=1,j-1, beta[i,d]) * prod(h=1,i-1, beta[h,j]) )^m[a][i,j] ))
Gamma = vector(n,a,matrix(n,k,i,j, ( prod(h=1,n,prod(d=j,k,alpha[h,d])*prod(d=j+1,k,alpha[h,d])) * prod(d=1,j,alpha[i,d])^(2*M+2) / g^(2*M+1) )^(m[a][i,j]) ))
Delta = vector(n,a,matrix(n,k,i,j, ( prod(h=1,n,prod(d=j,k, beta[h,d])*prod(d=j+1,k, beta[h,d])) * prod(d=1,j, beta[i,d])^(2*M+2) )^(m[a][i,j]) ))
\\\\\\\\\\\\
\\ ROUND3
@ -84,8 +84,7 @@ Phi = vector(n,a,matrix(n,k,i,j, prod(h=1,n,Delta[h][i,j])^x[a] ))
\\ winner matrix
v = matrix(n,k,a,j, prod(i=1,n,Gamma[i][a,j]) / prod(i=1,n,Phi[i][a,j]) )
vi = lift(v)
print("bids are: ", bid)
for(X=1,n, if(vecmin(vi[X,])==1, print("And the winner is ", X) ))
for(X=1,n, if(vecmin(vi[X,],&i)==1, print("And the winner is ", X, " with the price ", i) ))