Assignment:
A (finite) square matrix A = (ai,j )i,j is called anti-symmetric if ai,j = −aj,i for all i and j . Prove that if the payoff matrix of a two-player zero-sum game is antisymmetric, then the value of the game in mixed strategies is 0. In addition, Player I’s set of optimal strategies is identical to that of Player II, when we identify Player I’s pure strategy given by row k with Player II’s pure strategy given by column k.
Provide complete and step by step solution for the question and show calculations and use formulas.