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The game is as follows:

$$\begin{array}{c|c|c|} &A&B\\ \hline A&2;3&2;3\\ \hline B&-1;2&1;2\\ \hline C&-1;3&4;2\\ \hline \end{array}$$

I've written a program that calculates nash equilibria. Here is one that it calculated with the corresponding payoff vectors:

The greyed-out strategies are the mixed strategies. Is this equilibrium indeed valid? To me it seems to be valid, but I am not sure as other tools, such as Gambit, did not calculate this equilibrium. So is there something wrong with the algorithm I programmed or not?

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  • $\begingroup$ Could you say a little bit more about the snapshot ? $\endgroup$ – callculus Nov 5 '15 at 18:39
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It looks correct, but maybe the tools didn't calculate this particular one because it lies at the intersection of two families of Nash equilibria. The first family has

$$ P_1(B) = \begin{cases} 0 & p < 2/5 \\ q & p = 2/5 \\ 1 & p > 2/5 \end{cases} $$ $$ P_1(A, F) = \begin{cases} 1 & p < 2/5 \\ 1-q & p = 2/5 \\ 0 & p > 2/5 \end{cases} $$ $$ P_2(C) = p $$ $$ P_2(D) = 1-p $$

and the other family has

$$ P_1(B) = r $$ $$ P_1(A, F) = 1-r $$ $$ P_2(C) = 2/5 $$ $$ P_2(D) = 3/5 $$

where $p, q, r$ are arbitrary in $[0, 1]$.

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