Tom, Dick, and Harry play the following game. At the first stage, Dick or Harry is chosen, each with probability 1 2 . If Dick has been chosen, he plays the Game A in Figure 5.36, with Tom as his opponent. If Harry has been chosen, he plays the Game B in Figure 5.36, with Tom as his opponent. Tom, however, does not know who his opponent is (and which of the two games is being played). The payoff to the player who is not chosen is 0.
Do the following:
(a) Draw the extensive form of the game.
(b) Write down strategic form of the game.
(c) Find two equilibria in pure strategies.
(d) Find an additional equilibrium in mixed strategies.