Game Theory ( 2 player zero-sum game)

ruby_duby

Hi

I have just started a game theory module and have been given the following exercise. Can anyone help me with the following question. I have a feeling I can use a minimax argument to answer this but I am not sure how to go about this.

Suppose a two-player zero-sum game has the following matrix:
A =

a b
c d

Suppose that (e1; e1) is an equilibrium solution. Suppose K a member of the ℝ is a constant. Show for the new game matrix:
A0 =

a + K b + K
c + K d + K

that (e1; e1) is still the equilibrium solution.

ruby_duby

if i let Suppose a two-player zero-sum game has the following matrix:

A₁ =

a b
c d

then calculate e₂^TA₁e₁ = c

Then if I let A₂ =

a+k b+k
c+k d+k

then e₂^TA₂e₁ = c+k

but I have no idea if this is right or what to do next