Question

Solve the game with the payoff Matrix 2 6 -4 -7 4 7 -3 -5 3 3 9 8

Answer 1

Maximim for A=Max(Minimum in each Row)

1 Player B Minimum in each Row 1 II TV T -7 Player A I 2 6 - 4 - 7 47 -3-5 3 9 -5 حر 8 3 o Maximum in each Column → 4 7 8

=Max(-7,-5,3)

=3

Minimax of B=Min(Maximum in each column)

=Min(4,7,9,8)

=4

Maximum for A is called the lower value of the game and denoted by V and minimax of B is called the upper value of the game and denoted by $\bar{V}$

So here V=3 & $\bar{V}$ =4

If V is the value of the game then always satisfies the inequality

Maximim for minimax for B

A <

  $3\leq V \leq 4$

If $\bar{V}$ =V=V then saddle point exist

But here $\bar{V}$ $\neq$V

so, here saddle point is not exist.

Thank you ,

If any queries please leave your valuable comment on comment box

Please rate my answer as well