3. Two players, Alice and Bob, sit in separate rooms. They are not allowed to commu nicate. Each is asked to write a number on a piece of paper. The number must be an integer between 1 and 20. That is, the possible choices are 1, 2, 3, 4, 5, 6,7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 for each player. If they both write the same number, then they each win that amount of dollars (e.g., if both write down 3, each wins $3). If they write different numbers, then Alice wins nothing, but Bob wins 10 dollars (e.g., if Alice writes 3 and Bob writes 9, then Alice gets nothing but Bob wins $10). (a) (10 p.) How many Nash equilibria are there in this game? Explain your reasoning. (b) (5 p.) Is there any Nash equilibrium where a player uses a weakly dominated strategy? Explain