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

1 files changed, 17 insertions, 18 deletions

diff --git a/gp-scripts/m+1stPrice b/gp-scripts/m+1stPrice
index 8407e96..a6ac17c 100644
--- a/gp-scripts/m+1stPrice
+++ b/gp-scripts/m+1stPrice
@@ -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)
-
-\\\\\\\\\\\\
-\\ 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
+\\p = 263
+\\q = (p-1)/2
+\\ use save prime p
+q = prime(2^12)
+p = 2*q + 1
+
+\\ 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) ))