A two-player zero sum game in which [Si] = n for i = 1, 2 is called symmetric if A, the payoff matrix for Player 1 satisfies A = -AT. (a) In linear algebra, how do we classify A when A = -AT?

A two-player zero sum game in which [Si] = n for i = 1, 2 is called symmetric if A, the payoff matrix for Player 1 satisfies A = -AT. (a) In linear algebra, how do we classify A when A = -AT?

A two-player zero sum game in which [Si] = n for i = 1, 2 is called symmetric if A, the payoff matrix for Player 1 satisfies A = -AT. (a) In linear algebra, how do we classify A when A = -AT?

A two-player zero sum game in which [Si] = n for i = 1, 2 is called symmetric if A, the payoff matrix for Player 1 satisfies A = -AT. (a) In linear algebra, how do we classify A when A = -AT? (b) Does this definition of symmetric match the traditional definition of a symmetric game? Explain. (c) Suppose x is an optimal maximin strategy for Player 1 in a symmetric zero-sum game. Prove x is an optimal maximin strategy for Player 2 in this game. (d) Show that for any symmetric zero-sum game, the maximin value is zero.   Share this:TwitterFacebook

A two-player zero sum game in which [Si] = n for i = 1, 2 is called symmetric if A, the payoff matrix for Player 1 satisfies A = -AT. (a) In linear algebra, how do we classify A when A = -AT?

A two-player zero sum game in which [Si] = n for i = 1, 2 is called symmetric if A, the payoff matrix for Player 1 satisfies A = -AT. (a) In linear algebra, how do we classify A when A = -AT? (b) Does this definition of symmetric match the traditional definition of a symmetric game? Explain. (c) Suppose x is an optimal maximin strategy for Player 1 in a symmetric zero-sum game. Prove x is an optimal maximin strategy for Player 2 in this game. (d) Show that for any symmetric zero-sum game, the maximin value is zero.   Share this:TwitterFacebook