Can equal rows or columns be removed from a payoff matrix

Question

Since the definition for dominated rows or columns dictates equal and/ or greater or less than respectively, can we remove two rows that are equal or two columns that are equal? This seems arbitrary in how this would be done and thus the other player would not be able to deduce what the reduced payoff matrix would look like.

Answer 1

Yes and no. Yes if you want to find any equilibrium. No if you want to find all equilibriums.

For example if you take the zero matrix every point is an equilibrium, but if you remove all rows and columns you end up with exactly one equilibrium