1. Game Theory My dog, Maggie, and my brother's dog, Luna, love getting attention. They are very picky on who gives them attention though. They both prefer my mom over everyone else, then they prefer their owner over the other person (ie - Maggie prefers me over my brother). They also hate sharing attention. I defined their game below: Luna Me My Mom My Brother Me 3.2 2,8 6,6 Maggie My Mom 8,1 0,0 8,3 My Brother 1,3 1,8 2,3 a) If the dogs worked together, which option would they choose to maximize their joint utility? b) Find all Nash equilibria in the simultaneous move game. c) Let's suppose that Maggie gets to make the first move, then Luna gets to move after observing Maggie's choice. Setup the sequential move game. d) Solve the game in part c. What are the new Nash equilibria? e) Compare your answer from part b to part d. Why did your answers differ