Consider the following two-player game composed of two stages. In the first stage, one of the two following matrices is chosen by a coin toss (with each matrix chosen with probability 1/2). In the second stage, the two players play the strategic-form game whose payoff matrix is given by the matrix that has been chosen.
For each of the following cases, depict the game as an extensive-form game, and find the unique equilibrium:
(a) No player knows which matrix was chosen.
(b) Player I knows which matrix was chosen, but Player II does not know which matrix was chosen. What effect does adding information to Player I have on the payoffs to the players at equilibrium?