Two players, Jack and Jill, are put in separate rooms. Then each is told the rules of the game. Each is to pick one of six letters: G, K, L, Q, R, or W. If the two happen to choose the same letter,...

Two players, Jack and Jill, are put in separate rooms. Then each is told the rules of the game. Each is to pick one of six letters: G, K, L, Q, R, or W. If the two happen to choose the same letter, both get prizes as follows:

If they choose different letters, each gets 0. This whole schedule is revealed to both players, and both are told that both know the schedules, and so on.

(a) Draw the table for this game. What are the Nash equilibria in pure strategies?

(b) Can one of the equilibria be a focal point? Which one? Why?