I'm a computer science student and I have this problem I need to solve for my games theory course. I don't have an example to follow, or use as guidance, and my colleagues are not very helpful( as in, they have no interest in solving this).

I managed to solve a non constant sum problem, as I had an example for that one. But I can't wrap my head around this one.

So, here's the problem:

Consider a finite two person zero-sum game with a payoff matrix A which is a matrix of order 7. Further assume that the row sums and column sums are all equal to 28. Then find the value of the game and a pair of optimal strategies for the two players.}

Some help or guidance would be greatly appreciated! Maybe a solved problem(not necessarily this one), that I can use as an example would be even better, but I don't want to ask too much


  • 1
    $\begingroup$ see this for a bit on calculating the value: math.stackexchange.com/questions/239803/…. then you need to see what restrictions the row and column sums put on the matrix. I'm guessing that's the tricky part. $\endgroup$ – Trurl May 26 '14 at 13:15

The strategy profile in which both players uniformly randomly choose among the $7$ strategies is a Nash equilibrium. Since all row sums and all column sums are equal, neither player can change the expected payoff by switching strategies.


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