Information for questions 06 and 07 These next two questions serve as practice at solving sequential (tree form) games through backward induction. In all games, the payoff of player 1 (the first mover or leader) is shown on the left, and the payoff of player 2 (the second mover, or follower) is shown on the right. Question 06 Consider the game in question 04, but now assume it is played sequentially. The images below show the sequential game when Jane moves first (top), and when Joe moves first (bottom). Jane Joe Payoffs Chooses First Chooses Second (UJa, UJo) scott (3, 3) scott Joe dodge (0, 0) Jane scott (0, 0) dodge Joe dodge (1, 1) Joe Jane Payoffs Chooses First Chooses Second (UJo, UJa) scott (3, 3) scott Jane dodge (0, 0) Joe scott (0, 0) dodge Jane dodge (1, 1) Which of the following alternatives is correct? (a) The equilibrium in both cases is (Dodge, Dodge) (b) The equilibrium in both cases is (Scott, Scott) (c) In both cases, the first mover has an advantage (d) In both cases, the second mover has an advantageQuestion 07 Consider the game in question 05, but now assume it is played sequentially. The images below show the sequential game when Anna moves first (top), and when Brian moves first (bottom). Anna Brian Payoffs Chooses First Chooses Second (UA, UD) jame (5, 3) game Brian movie (2, 2) Anna game (1, 1) movie Brian movie (3, 5) Brian Anna Payoffs Chooses First Chooses Second (We, UA) game (3, 5) game Anna movie (1, 1) Brian game (2, 2) movie Anna movie (5, 3) Which of the following alternatives is correct? (a) When Anna moves first, the equilibrium is (Movie, Movie) (b) When Brian moves first, the equilibrium is (Game, Game) (c) In both cases, the first mover has an advantage (d) In both cases, the second mover has an advantageInformation for questions 08 and 09 Back to the "Battle of the Sexes" example, imagine that Brian is mad at Anna for some silly reason. For as long as he is mad at her, he will not enjoy her company as before. On top of whatever utility level he was getting from doing activities with Anna, Brian now experiences a discomfort equivalent to -5 utility units. The modified simultaneous game (normal form) is shown below. Anna Game Movie 5 Game -2 Brian 2 Movie Hint: Drawing the corresponding tree form game for each situation will help you find the answers. Question 08 Consider a situation in which the game above is played sequentially and Brian is the first mover. Which of the following alternatives is correct? (a) The equilibrium is (Brian chooses Movie, Anna choses Game) (b) The equilibrium is (Brian chooses Movie, Anna choses Movie) (c) The equilibrium is (Brian chooses Game, Anna choses Game) (d) The equilibrium is (Brian chooses Game, Anna choses Movie) Question 09 Consider a situation in which the game above is played sequentially and Anna is the first mover. Which of the following alternatives is correct? (a) The equilibrium is (Anna chooses Game, Brian choses Game) (b) The equilibrium is (Anna chooses Movie, Brian choses Game) (c) There is a first mover advantage in this game (d) There is a second mover advantage in this game