public override string[] Execute()
{
resultComment.Remove(0, resultComment.Length);
List <string> resultSet = new List <string>();
foreach (Strategies.Wins w in strategies.WinsList)
{
// Check if w is in alpha-kernel
bool inAlphaKernel = true;
for (int t = 1; t < (1 << strategies.PlayerCount) - 1; t++)
{
// t is a coalition.
int[] coalition = new int[CountBits(t)];
int[] complementary = new int[strategies.PlayerCount - CountBits(t)];
int[] index = new int[strategies.PlayerCount];
List <string> tmp = new List <string>(w.Key.Replace(',', ' ').Split(' '));
tmp.RemoveAll(string.IsNullOrEmpty);
string[] st = tmp.ToArray();
for (int j = 0; j < index.Length; j++)
{
index[j] = strategies.GetStrategies(j).IndexOf(st[j]);
}
int p = 0, q = 0;
int coalitionVariants = 1;
for (int j = 0; j < strategies.PlayerCount; j++)
{
if ((t & (1 << j)) != 0)
{
coalition[p++] = j;
coalitionVariants *= strategies.GetStrategies(j).Count;
}
else
{
complementary[q++] = j;
}
}
int[] newIndex = new int[strategies.PlayerCount];
for (int newT = 0; newT < coalitionVariants; newT++)
{
int k;
k = newT;
for (int i = 0; i < coalition.Length; i++)
{
int v = strategies.GetStrategies(coalition[i]).Count;
newIndex[coalition[i]] = k % v;
k /= v;
}
bool isBetter = true;
for (int threat = 0; threat < strategies.WinsList.Count / coalitionVariants; threat++)
{
k = threat;
for (int i = 0; i < complementary.Length; i++)
{
int v = strategies.GetStrategies(complementary[i]).Count;
newIndex[complementary[i]] = k % v;
k /= v;
}
Strategies.Wins w1 = strategies.GetWins(IndexArrayToKey(newIndex));
bool allEqual = true;
for (int i = 0; i < coalition.Length; i++)
{
int c = coalition[i];
allEqual &= w1[c] == w[c];
if (w1[c] < w[c])
{
isBetter = false;
break;
}
}
if (isBetter && allEqual)
{
isBetter = false;
}
if (!isBetter)
{
break; // Already found good threat.
}
}
if (isBetter)
{
inAlphaKernel = false;
resultComment.AppendFormat("{0} не належить α-ядру гри, так як гравці {{1}} можуть утворити коаліцію", w.Key, PlayerSet(coalition));
break;
}
}
if (!inAlphaKernel)
{
break;
}
}
if (inAlphaKernel)
{
resultComment.Append(w.Key + " належить α-ядру гри\r\n");
resultSet.Add(w.Key);
}
}
return(resultSet.ToArray());
}
public override string[] Execute()
{
resultComment.Remove(0, resultComment.Length);
List <string> resultSet = new List <string>();
foreach (Strategies.Wins w in strategies.WinsList)
{
// Check if w is in beta-kernel
bool inBetaKernel = true;
for (int t = 1; t < (1 << strategies.PlayerCount) - 1; t++)
{
// t is a coalition.
int[] coalition = new int[CountBits(t)];
int[] complementary = new int[strategies.PlayerCount - CountBits(t)];
int[] index = new int[strategies.PlayerCount];
List <string> tmp = new List <string>(w.Key.Replace(',', ' ').Split(' '));
tmp.RemoveAll(string.IsNullOrEmpty);
string[] st = tmp.ToArray();
for (int j = 0; j < index.Length; j++)
{
index[j] = strategies.GetStrategies(j).IndexOf(st[j]);
}
int p = 0, q = 0;
int coalitionVariants = 1;
for (int j = 0; j < strategies.PlayerCount; j++)
{
if ((t & (1 << j)) != 0)
{
coalition[p++] = j;
coalitionVariants *= strategies.GetStrategies(j).Count;
}
else
{
complementary[q++] = j;
}
}
int[] newIndex = new int[strategies.PlayerCount];
for (int newT = 0; newT < strategies.WinsList.Count / coalitionVariants; newT++)
{
int k;
k = newT;
for (int i = 0; i < complementary.Length; i++)
{
int v = strategies.GetStrategies(complementary[i]).Count;
newIndex[complementary[i]] = k % v;
k /= v;
}
bool isGoodThreateningStrategy = true;
for (int forw = 0; forw < coalitionVariants; forw++)
{
k = forw;
for (int i = 0; i < coalition.Length; i++)
{
int v = strategies.GetStrategies(coalition[i]).Count;
newIndex[coalition[i]] = k % v;
k /= v;
}
Strategies.Wins w1 = strategies.GetWins(IndexArrayToKey(newIndex));
bool allEqual = true;
for (int i = 0; i < coalition.Length; i++)
{
int c = coalition[i];
allEqual &= w1[c] == w[c];
if (w1[c] < w[c])
{
isGoodThreateningStrategy = false;
break;
}
}
if (isGoodThreateningStrategy && allEqual)
{
isGoodThreateningStrategy = false;
}
if (!isGoodThreateningStrategy)
{
break; // Already found good threat.
}
}
if (!isGoodThreateningStrategy)
{
inBetaKernel = false;
// resultComment.AppendFormat("{0} не належить β-ядру гри", w.Key);
break;
}
}
if (!inBetaKernel)
{
break;
}
}
if (inBetaKernel)
{
// resultComment.Append(w.Key + " належить β-ядру гри\r\n");
resultSet.Add(w.Key);
}
}
if (resultSet.Count > 0)
{
resultComment.Append("β-ядро гри: {");
for (int i = 0; i < resultSet.Count; i++)
{
if (i > 0)
{
resultComment.Append(", ");
}
resultComment.Append(resultSet[i]);
}
resultComment.Append("}");
}
else
{
resultComment.Append("β-ядро гри порожнє");
}
return(resultSet.ToArray());
}
public override string[] Execute()
{
resultComment.Remove(0, resultComment.Length);
List <string> resultSet = new List <string>();
foreach (Strategies.Wins w in strategies.WinsList)
{
// Check if w is Strong Nash Equibalance
bool isStrongNash = true;
for (int t = 0; t < (1 << strategies.PlayerCount) - 1; t++)
{
int[] group = new int[CountBits(t)];
int[] index = new int[strategies.PlayerCount];
List <string> tmp = new List <string>(w.Key.Replace(',', ' ').Split(' '));
tmp.RemoveAll(string.IsNullOrEmpty);
string[] st = tmp.ToArray();
for (int j = 0; j < index.Length; j++)
{
index[j] = strategies.GetStrategies(j).IndexOf(st[j]);
}
int p = 0;
for (int j = 0; j < strategies.PlayerCount; j++)
{
if ((t & (1 << j)) != 0)
{
group[p++] = j;
}
}
int v = 1;
for (int j = 0; j < group.Length; j++)
{
v *= strategies.Count(group[j]);
}
for (int i = 0; i < v; i++)
{
int k = i;
for (int j = 0; j < group.Length; j++)
{
index[group[j]] = k % strategies.Count(group[j]);
k /= strategies.Count(group[j]);
}
string key = IndexArrayToKey(index);
Strategies.Wins w1 = strategies.GetWins(key);
bool allNotWorse = true, haveBetter = false;
for (int j = 0; j < group.Length; j++)
{
if (w1[j] < w[j])
{
allNotWorse = false;
break;
}
else
if (w1[j] > w[j])
{
haveBetter = true;
}
}
if (allNotWorse && haveBetter)
{
isStrongNash = false;
resultComment.Append(w.Key);
resultComment.Append(" не є Сильною Рівновагою Неша, бо коаліція {");
for (int j = 0; j < group.Length; j++)
{
if (j > 0)
{
resultComment.Append(", ");
}
resultComment.Append(group[j] + 1);
}
resultComment.Append("} змінює стратегію на ");
resultComment.Append(w1.Key);
resultComment.Append("\r\n");
break;
}
}
if (!isStrongNash)
{
break;
}
}
if (isStrongNash)
{
resultComment.Append(w.Key + " є Сильною Рівновагою Неша\r\n");
resultSet.Add(w.Key);
}
}
return(resultSet.ToArray());
}