complete assoclatea Lanvas (quUIZ by 100U AN on KFriaay, 4/20/2u0.4 1. The following payoff matrix describes the strategic situation faced by two rowdy teens, Ace and Vince, who are driving cars towards each other in a (simultaneous move) game of \"Chicken\". If both swerve at the last second, they avoid a collision. If only one swerves, they again avoid a collision and, in addition, the one who swerves (does not swerve) receives a psychological loss (gain) from being \"wimpy (\"tough\"). If neither swerves, they each suffer a large loss from the resulting collision. Vince Swerve Don't Swerve Ace Swerve Don't Swerve a. Find the two pure strategy Nash equilibria of this game. b. Find the mixed strategy Nash equilibrium of this game. . Write down both the normal form and the extensive form of the sequential version of this game in which Ace is able to (publicly) commit to his action before Vince chooses his action. As the second mover, what are Vince's four possible strategies? d. What are the three pure strategy Nash equilibria of the sequential version of the *Chicken\" game 1n (c)? e. What is the unique subgame perfect Nash equilibrium of the sequential version of the \"Chicken\" game in (c)? 2. Rocky's and Bullwinkle's are the only fish bait shops in Moosehead, ME. The daily inverse market demand curve for fish bait in Moosehead is p = 7 0.1(y; + ,). The marginal cost of supplying a unit of fish bait is $1 for both shops. a. Find the equilibrium price of a unit of fish bait and the number of units sold per day by each shop 1f they compete as Cournot duopolists. Also, compute daily consumer surplus and daily profit on fish bait for each shop. b. Suppose that the two bait shops act as a profit-maximizing fish bait cartel. Find the equilibrium price of a unit of fish bait and the number of units sold per day by the cartel. Compute daily consumer surplus. Also, compute each shop's daily output and profit if each shop supplies half of the total quantity of fish bait supplied by the cartel. c. Write down the payoff matrix facing the two bait shops if each decides between just two possible quantity choices: (1) supply exactly half of the profit-maximizing total quantity of the cartel or (ii) supply the profit-maximizing Cournot quantity. d. Find the Nash equilibrium of one round of play of the game whose payoff matrix you wrote down in (). What do you conclude about the stability of the cartel outcome in a single round of play? e. Now suppose that the game in () 1s repeated for an indeterminate number of times. Each shop assumes that the other will adhere to the cartel agreement as long as it hasn't been cheated on, but will switch to the Cournot output level forever if it ever is cheated on. Show that the cartel outcome is a subgame perfect Nash equilibrium if the bait shops do not dicconnt the future too much