Summer 2016Instructor: Akio YamazakiAssignment 2? Due date: August 10th, 2016? Work alone or in groups of TWO (maximum). Turn in the assignments individually.? Please write down how you arrived to your conclusions. If reasoning is rigorous and correct,you will get partial credits even if the answer is not.? If you have problems, you can ask me during my office hours or ask TA during her officehours, but please do not expect me or her to solve the problem for you or tell you thesolution. Please do not email me or TA about the assignment.Question 1: NE vs. BIE (15 points)Consider the following game: Player 1 makes a choice of either U or D. After observing player 1?schoice, player 2 chooses either L or R. If player 1 chooses U, player 2?s choice of L yeilds a payoffof (0, 0), where the first number is the payoff to player 1 and the second number is the playoff toplayer 2. Alternatively, if player 2 chooses R, the players receives a payoff of (5, 7). If player 1chooses D, player 2 generates payoff (4, 4) from choosing L and (6, 4) from choosing R.(a) Specify the strategy set for each player(b) Write down the normal form of representation of this game, and find the Nash equilibria(c) Write down the extensive form of representation of this game, and fine the Backward Induc-tion equilibriaQuestion 2: NE vs. SPNE (15 points)Consider the following game:Z W1C6, 4D3, 22B A2X4, 6Y2, 11X3, 0Y8, 511(a) Is this a perfect information game or imperfect information game?(a) How many sub-games are there?(b) Find the Nash equilibria(c) Find Sub-game Perfect Nash equilibriaQuestion 3: Envy ? a capital sin (15 points)Consider the following ultimatum bargaining game. There is 1 unit of a good and player 1 offersa split (x, 1 ? x), where x 2 [0, 1] is chosen by player 1. Player 2 accepts the offer (Y ) or refuse it(N). If player 2 accepts the offer, then player 1 gets x and player 2 gets 1 ? x. If player 2 refusesthe offer, then both players get 0. We assume that when player 2 is indifferent between acceptingand refusing, then he accepts.(a) Suppose that each player maximizes his payoff. Find the Backward Induction Equilibrium.Suppose now players are envious. More precisely, the utility of player 1 is equal to his payoff minus times the payoff of player 2 and the utility of player 2 is equal to his payoff minus times thepayoff of player 1, with > 0. The parameter can therefore be interpreted as a measure of?envy.?(b) Find the BIE as a function of .(c) Interpret.Question 4: Strategic Investment (15 points)Recall that in the class, we have analyzed ?Strategic Investment? game where two firms, firm 1and firm 2, are competing in the Cournot model fashion. But we added an additional decisionmaking for firm 1 prior to the competition. That is firm 1 can choose to rent a new machine thatwill lower his costs by 50%. It will cost \$d (million) to rent this new machine. Both firms face alinear demand curve, p = 4 ? Q where Q = q1 + q2. We assume that each firm?s marginal cost is1, i.e., it costs \$1 per unit of output.(a) Find Nash equilibrium quantities (bq1, bq2) and equilibrium profits (b1, b2) in the subgamewhere firm 1 has decided to rent the new machine.(b) Find sub-game perfect equilibria of this game. [Hint: You will have to find a condition ford.]Solution details:STATUS Answered QUALITY Approved ANSWER RATING This question was answered on: Apr 19, 2020 PRICE: \$15 Solution~000.zip (25.37 KB) Buy this answer for only: \$15 This attachment is locked × Please Enter The Email Where You Want To Receive Solution. Get this solution for only: \$

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