# Is it possible to make excluded search with for loop in Java? [closed]

I am trying to calculate all pure strategy Nash equilibrium in a mxn game. It requires to check all pure strategy pairs (m.n pairs). Suppose player 1 has m strategies. Algorithm should start with the first pair (1,1) and compare (1,1) with (2,1),(3,1),...(m,1).

Same for all strategies, exp: (3,4) is compared by (1,4),(2,4),(4,4),...,(m,4).

In summary is it possible to make a search with for loop which excludes existing i:

Thank you.

• Programming questions are offtopic here.
– Raphael
Feb 16 '15 at 13:18

First of all, if you want to check each combination of pure strategies, you will have two nested for loops:

int a, b;
for (b = 0; b < n; b++) {
for (a = 0; a < m; a++) {
compare(a, b);
}
}


Additionally, compare(a,b) will then be compared to each alternative I have to exchange a under the assumption that my opponent will use b:

int compare(int a, int b) {
for (int x = 0; x < m; x ++) {
if (x == a) continue; // This will exclude the check (a, b), (a, b)
System.out.println("Comparing (" + a + ", " + b ") and (" + x + ", " + b + ")");
}
return 0;
}


However, my knowledge of game theory is a little bit rusted. Aren't you trying to determine the best answer in pure strategies to each pure strategy of your opponent?

In fact, this comparison would have a complexity of $\mathcal{O}(m^2\cdot n)$. In order to determine the best answers with only a complexity of $\mathcal{O}(m\cdot n)$, you can gradually search the maximum payoff while traversing each possible combination of strategies:

int best_answers[n];
int a, b;
int max_payoff;
for (b = 0; b < n; b++) {
max_payoff = 0; // If negative payoffs are possible, adjust this.
for (a = 0; a < m; a++) {
if (payoff[a][b] > max_payoff) {
max_payoff = payoff[a][b];

Here, I assume that int payoff[m][n] is a 2-dimensional array that encodes the payoff matrix. After running this algorithm, best_answers[b] contains the best answer strategy for strategy $0 \leq b < n$ of the opponent.