15. [20 pts] Buster and Lucille and deciding whether to attend the talent show "Motherboy" or attend a local singles "Auction". Buster and Lucille both want to attend different events but also prefer to go together. The payoffs associated with each possible outcome are: (Lucille's payoffs listed first and Buster's second within in each cell) Lucille - Motherboy Lucille - Auction Buster - Motherboy Buster - Auction 0,0 4, 1 1,4 0,0 a) Assuming Lucille and Buster make their choice simultaneously, does either Lucille or Buster have a dominant strategy? If so what is it. b) How many Nash Equilibria are in the simultaneous game? What are they? (remember players can use pure or mixed strategies) c) Now this game is modified where Lucille gets to move first, and then Buster observes this move and makes his choice. Write out this new game in the extensive form and predict what actions each player will choose in this case. d) How much would Buster be willing to pay in order to become the first-mover instead of Lucille in part c). EXPLAIN YOUR ANSWER.