Problem Set #1 1._(20 points) Consider the following game: Player B Left Middle Right Top 7,17 21,21 14,11 Player A Middle 10,5 14,4 4,3 Bottom 4,4 7,3 10,25 a. Does either player have a dominant strategy? What about a dominated strategy? b. What are the Nash equilibria of this game? c. Is there one Nash equilibrium that you think is a more likely outcome than the others? If so, why? If not, why not? d. Now suppose the game looks like this: Player B Left Middle Right Top 7,17 15,21 14,11 Player A Middle 10.5 14,4 4,3 Bottom 4,4 73 13,25 Have the Nash equilibria changed from before? e. Which outcome would Player B prefer to happen? Why wouldn't it happen? Is there anything (outside the game) she could do to achieve it? Can you think of any (legal or not) real-world analogs to this scenario