private static double GlobalPr(GlobalState s, int[] a)
{
double prob = 1;
for (int i = 0; i < n; i++)
{
if (!bybool[i])
{
prob *= Pr(i, s, a);//use the independance of probability
}
}
return(prob);
}
private static GlobalState BT(GlobalState s, int[] a, List <GlobalState> gstates)
{
State[] localstates = new AState[n];
for (int i = 0; i < n; i++)
{
AState aS = (AState)(s.getLocalStates()[i]);
int label = aS.getLabel();
int l = aS.getL();
int[] c = aS.getC();
int[] aSData = new int[n + 2];
if (label != 2)
{
int shootcount = 0;
for (int j = 0; j < n; j++)
{
if (j != i && a[j] == (i + 1))//convert zero based index of players to one based index for shooting
{
shootcount++;
if (c[j] > 0)//lose confidence with shootings
{
c[j]--;
}
}
aSData[j] = c[j];
}
l = Math.Max(0, l - shootcount);
label = (label + 1) % 3;
aSData[n] = l;
aSData[n + 1] = label;
}
else
{
for (int j = 0; j < n; j++)
{
if (j != (i))//update confidence
{
c[j] = Math.Min(2, c[j] + 1);
}
aSData[j] = c[j];
}
l = 2;//restore life
label = (label + 1) % 3;
aSData[n] = l;
aSData[n + 1] = label;
}
localstates[i] = new AState(i, aSData);
}
return(gstates[getGlobalStateIndex(localstates)]);
}
private static double Pr(int i, GlobalState s, int[] a)
{
AState aS = (AState)(s.getLocalStates()[i]); //retrive the state of player i
int[] c = aS.getC(); //retrive confidence list of player i
double normal_sum = 0;
double maxcij = 0;
for (int j = 0; j < n; j++)
{
AState aSj = (AState)(s.getLocalStates()[j]);
if (j != i)
{
if (aSj.getL() > 0) //only the living ones are considered for shooting
{
if (c[j] > maxcij) //find max confidence value
{
maxcij = c[j];
}
normal_sum += c[j];
}
}
}
if (normal_sum > 0)//if some other player is alive
{
if (a[i] == 0)
{
return(1 - maxcij / (normal_sum));
}
else
{
for (int j = 1; j <= n; j++)
{
if (a[i] == j)
{
AState aSj = (AState)(s.getLocalStates()[j - 1]);//shift the index of j
int lj = aSj.getL();
if (lj == 0)
{
return(0);
}
else
{
return((maxcij * c[j - 1]) / normal_sum);//shifting the index to zero based
}
}
}
}
}
else //if no other player is alive
{
if (a[i] == 0)
{
return(1);
}
else
{
return(0);
}
}
return(0);
}
private static String Nashepdeltamul(List <double>[] vcurrent, List <double>[] vprev, List <double>[] ucurrent, List <double>[] uprev, int i0, int j0)
{
String result = "";
double min_distance = 20, deltastar = 0;
List <int> ratlist = new List <int>();
ratlist.Add(i0);
ratlist.Add(j0);
while (result.Equals("undecided") || result.Equals(""))
{
//initialize vi and ui
for (int i = 0; i < n; i++)
{
vcurrent[i] = new List <double>();
vprev[i] = new List <double>();
ucurrent[i] = new List <double>();
uprev[i] = new List <double>();
for (int s = 0; s < gstates.Count; s++)
{
vcurrent[i].Add(0);
vprev[i].Add(0);
ucurrent[i].Add(0);
uprev[i].Add(0);
}
}
//algo
double M = 4;
//beta^k < (1-beta)*delta/5M
//k>log((1-beta)*delta/5M)/log(beta)
double k = Math.Ceiling(Math.Log(((1 - beta) * delta) / (24 * M)) / Math.Log(beta));
double EiK = (6 * M * Math.Pow(beta, k)) / (1 - beta);
System.Diagnostics.Debug.WriteLine("k =" + k);
Parallel.For(0, gstates.Count, index =>
// Parallel.For(0, 729, index =>
{
GlobalState s = gstates[(index * 128) % gstates.Count];
// GlobalState s = gstates[(index * 128) % 729];
for (int t = 0; t < k; t++)
{
// foreach (int i in ratlist)//i,j rationals
// {//for each altruistic player, player of interest is rational
bybool[i0] = true; //make i byzantine
bybool[j0] = true; //make j byzantine
double max = 0;
foreach (GlobalAction a_ij in multiAc)//for each action of rational ij 2
{
double minbyzi = 20;
double minbyzj = 20;
foreach (GlobalAction a_z in byzAc)//for each byz action Z
{
double rewardi = 0;
double rewardj = 0;
foreach (GlobalAction a_al in AlmrAc) //for each altruistic action,two rat players Al-2
{
setglobalAction(i0, j0, a_ij, a_z, a_al); //call overridden method
if (BT(s, Actions, gstates) != null)
{
GlobalState snext = BT(s, Actions, gstates);
rewardi += GlobalPr(s, Actions) * (H(i0, s, Actions) + beta * vprev[i0][getGlobalStateIndex(snext.getLocalStates())]);
rewardj += GlobalPr(s, Actions) * (H(j0, s, Actions) + beta * vprev[j0][getGlobalStateIndex(snext.getLocalStates())]);
}
}//expected reward calculated for a_z,a_ij
if (AlmrAc.Count == 0)
{
setglobalAction(i0, j0, a_ij, a_z, null);//call overridden method
if (BT(s, Actions, gstates) != null)
{
GlobalState snext = BT(s, Actions, gstates);
rewardi = (H(i0, s, Actions) + beta * vprev[i0][getGlobalStateIndex(snext.getLocalStates())]);
rewardj = (H(j0, s, Actions) + beta * vprev[j0][getGlobalStateIndex(snext.getLocalStates())]);
}
}
if (rewardi < minbyzi)
{
minbyzi = rewardi;
}
if (rewardj < minbyzj)
{
minbyzj = rewardj;
}
//min reward calculated for each a_ij
// System.Diagnostics.Debug.WriteLine("reward =" + minbyz);
}//minbyz calculated
if (byZ.Count == 0)
{
double rewardi = 0;
double rewardj = 0;
foreach (GlobalAction a_al in AlmrAc) //for each altruistic action,two rat players Al-2
{
setglobalAction(i0, j0, a_ij, null, a_al); //call overridden method
if (BT(s, Actions, gstates) != null)
{
GlobalState snext = BT(s, Actions, gstates);
rewardi += GlobalPr(s, Actions) * (H(i0, s, Actions) + beta * vprev[i0][getGlobalStateIndex(snext.getLocalStates())]);
rewardj += GlobalPr(s, Actions) * (H(j0, s, Actions) + beta * vprev[j0][getGlobalStateIndex(snext.getLocalStates())]);
}
} //expected reward calculated for a_z,a_ij
if (AlmrAc.Count == 0)
{
setglobalAction(i0, j0, a_ij, null, null); //call overridden method
if (BT(s, Actions, gstates) != null)
{
GlobalState snext = BT(s, Actions, gstates);
rewardi = (H(i0, s, Actions) + beta * vprev[i0][getGlobalStateIndex(snext.getLocalStates())]);
rewardj = (H(j0, s, Actions) + beta * vprev[j0][getGlobalStateIndex(snext.getLocalStates())]);
}
}
minbyzi = rewardi;
minbyzj = rewardj;
//min reward calculated for each a_ij
// System.Diagnostics.Debug.WriteLine("reward =" + minbyz);
}
/* if (minbyz > max)
* max = minbyz;
* exp += Pr(i, s, Actions) * minbyz;*/
//min reward is used to maximize a different reward function
if (alpha * minbyzi + (1 - alpha) * minbyzj > max)
{
max = alpha * minbyzi + (1 - alpha) * minbyzj;
vcurrent[i0][getGlobalStateIndex(s.getLocalStates())] = minbyzi;
vcurrent[j0][getGlobalStateIndex(s.getLocalStates())] = minbyzj;
}
}//maxrat calculated
// vcurrent[i0][getGlobalStateIndex(s.getLocalStates())] = max;//v^k_i(s)=maxminE
// ucurrent[i][getGlobalStateIndex(s.getLocalStates())] = exp;//v^k_i(s)=maxminE
bybool[i0] = false; //remove byzantine role from i
bybool[j0] = false; //remove byzantine role from i
vprev[i0] = vcurrent[i0];
vprev[j0] = vcurrent[j0];
}
});
double[] bigDelta = new double[n];
double ep1, ep2;
int countfail = 0;
int countpass = 0;
double distance = 0;
double minxy = 20;
bigDelta[ratlist[0]] = vcurrent[ratlist[0]][getGlobalStateIndex(gstates[0].getLocalStates())] - ucurrent[ratlist[0]][getGlobalStateIndex(gstates[0].getLocalStates())];
bigDelta[ratlist[1]] = vcurrent[ratlist[1]][getGlobalStateIndex(gstates[0].getLocalStates())] - ucurrent[ratlist[1]][getGlobalStateIndex(gstates[0].getLocalStates())];
double epi1, epi2, epj1, epj2;
epi1 = bigDelta[ratlist[0]] - 2 * EiK;
epi2 = bigDelta[ratlist[0]] + 2 * EiK;
epj1 = bigDelta[ratlist[1]] - 2 * EiK;
epj2 = bigDelta[ratlist[1]] + 2 * EiK;
if ((epi1 >= 0 && epj1 > eps) || (epj1 >= 0 && epi1 > eps))
{
return("unstable");
}
else if (epi2 <= eps && epj2 <= eps)
{
return("stable with eps" + eps);
}
else if (epi1 <= eps && epj1 <= eps)
{
return("stable with epsdel" + (eps + delta));//if (eps <= epi2 || eps <= epj2)
}
else
{
distance = Math.Sqrt(Math.Pow(epi2 - eps, 2) + Math.Pow(epj2 - eps, 2));
if (distance < min_distance)
{
min_distance = distance;
deltastar = Math.Min(Math.Abs(epi2 - eps), Math.Abs(epj2 - eps));
}
result = "undecided";
}
alpha += 0.2;
if (alpha >= 1)
{
return("NEepsdelta*" + " " + deltastar);
}
}
// System.Diagnostics.Debug.WriteLine(result);
return(result);
}
private static void reward_calc(List <double>[] prev, List <double>[] current, int i, bool biz)
{
/* Parallel.ForEach(gstates, (s) =>
* {*/
Parallel.For(0, gstates.Count, index =>
{
if (_debug)
{
Console.WriteLine(System.Threading.Thread.CurrentThread.ManagedThreadId);
}
GlobalState s = gstates[(index * 128) % gstates.Count];
//GlobalState s = gstates[(index * 128)%59049];
double max = 0;
double exp = 0;
foreach (int a_i in localactionset[i])//for each action of rational i
{
double minbyz = 20;
if (byzAc.Count == 0)// if no byzantines
{
double reward = 0;
// double ureward = 0;
foreach (GlobalAction a_al in AlrAc)//for each altruistic action Al-i
{
setglobalAction(i, a_i, a_al);
if (BT(s, Actions, gstates) != null)
{
GlobalState snext = BT(s, Actions, gstates);
reward += GlobalPr(s, Actions) * (H(i, s, Actions) + beta * prev[i][getGlobalStateIndex(snext.getLocalStates())]);
// ureward += GlobalPr(s, Actions) * (H(i, s, Actions) + beta * uprev[i][getGlobalStateIndex(snext.getLocalStates())]);
}
}//expected reward calculated for a_z,a_i
minbyz = reward;
}
else
{
foreach (GlobalAction a_z in byzAc)//for each byz action Z
{
double reward = 0;
// double ureward = 0;
foreach (GlobalAction a_al in AlrAc)//for each altruistic action Al-i
{
setglobalAction(i, a_i, a_z, a_al);
if (BT(s, Actions, gstates) != null)
{
GlobalState snext = BT(s, Actions, gstates);
reward += GlobalPr(s, Actions) * (H(i, s, Actions) + beta * prev[i][getGlobalStateIndex(snext.getLocalStates())]);
// ureward += GlobalPr(s, Actions) * (H(i, s, Actions) + beta * uprev[i][getGlobalStateIndex(snext.getLocalStates())]);
}
}//expected reward calculated for a_z,a_i
if (reward < minbyz)
{
minbyz = reward;
}
// System.Diagnostics.Debug.WriteLine("reward =" + minbyz);
}//minbyz calculated
}
if (minbyz > max)
{
max = minbyz;
}
exp += Pr(i, s, Actions) * minbyz;
}//maxrat calculated
if (biz)
{
current[i][getGlobalStateIndex(s.getLocalStates())] = max;//v^k_i(s)=maxminE
}
else
{
current[i][getGlobalStateIndex(s.getLocalStates())] = exp;//v^k_i(s)=maxminE
}
});
}