Alice and Bob are playing a game in which each of them has three strategies, A, B, or C.

If their choices do not match (e.g., if Alice picks B and Bob picks C), then no money is

exchanged; otherwise Alice pays Bob $6 (if they both choose A), or $3 (if they both choose

B), or $1 (if they both choose C). Is this a zero-sum game? Find a mixed-strategy Nash

equilibrium for it. Is this the only equilibrium of this game?