# Betting : murty's example of betting problem
# ( Murty in Linear complementarity..., Heldermann 1998, Ex 10.15)
# written in AMPL by Yu-Ju Kuo and Hans D. Mittelmann, 6/2001 
param N;
param NH;
param NG;
param BB;
param QQ;
param WI{1..N};
param PI{1..N};
param PP:=sum{i in 1..N}PI[i];
param WW:=sum{i in 1..N}WI[i];
param QI{i in 1..N}:=WI[i]/WW;;
var X{i in 1..N}:=i;     
var Term=(PP+sum{i in 1..N}X[i])*QQ;
var XIJ{i in 1..N,j in 1..N}=if(i==j) then 0 else X[i]/(X[i]+PI[i])+X[j]/(X[j]+PI[j]);
var SX{i in 1..N,j in 1..N}=if(i==j)then 0 else sum{k in 1..N}X[k]-X[i]-X[j];
var FIJ{i in 1..N,j in 1..N}=if(i==j) then 1 else 0.5*(Term-X[i]-X[j]-PI[i]-PI[j])*XIJ[i,j]+BB-SX[i,j];
minimize obj:-sum{i in 1..N}(sum{j in 1..N}QI[i]*QI[j]/(1-QI[i])*log(FIJ[i,j]));
s.t. gx1: BB-sum{i in 1..N}X[i]>=0;
s.t. gx2{i in 2..NG}:X[i-1]-1.e-10>=0;


data;

param N:=8;
param NH:=0;
param NG:=9;
param PI:=
1 4000
2 4000
3 4000
4 8000
5 3000
6 8000
7 13000
8 5000;
param BB:=500;
param QQ:=.83;
param WI:=
1 10000.
2 15000
3 5000
4 35000
5 5000
6 10000
7 18000
8 12000;