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- Consider a setting in which player 1 moves first by choosing among threeactions: a, b, and c. After observing the choice of player 1, player 2 choosesamong two actions: x and y. Consider the following three variants as towhat player 3 can do and what she knows when she moves:a. If player 1 chose a, then player 3 selects among two actions: high andlow. Player 3 knows player 2’s choice when she moves. Write down theextensive form of this setting. (You can ignore payoffs.)b. If player 1 chose a, then player 3 selects among two actions: high andlow. Player 3 does not know player 2’s choice when she moves. Writedown the extensive form of this setting. (You can ignore payoffs.)c. If player 1 chose either a or b, then player 3 selects among two actions: high and low. Player 3 observes the choice of player 2, but not that of player 1. Write down the extensive form of this setting.(You can ignore payoffs.)Consider a Variant oF the ultimatum qame We Studicd inclass in which players have Fairness considerations . The timing OF the qame is vSual. First , Player 1 propasar the split (100 -x", x) OF a hundred dellars to player 2,Where XE [0,100]. Player 2 observes split & decides whether to accept (in which case they recieve Money accor ding ti proposed Split) or reject (in Which Case they both get žero dollars).But now player i's Utility equals to her monetary Vtility minus the disutility From unFairneas proportional tO the differene in Monetary OutcCOMeS . That is, qiven a Final Split (m. ,m.) ket u, (m. ,m.) = m, -P. (m, - m2)" %3D U. (m. ,m2) = m,- P2 (m,-m.) Where PP are parametens of the game indicating how strongly Players care a bout Fairness. Note that the case we considered corres pends to B, = B2 = 0 (a) Let B, = To ,P2 = alcept ? revect ? Describe all seguentially rational Strategies For player 2. b) Let B, = 10 ,$=0. For each sequentially rational Strategy of player 2 yoU…You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…
- Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.Consider the game below with a worker (W) and a firm (F). The worker initially can choose to acquire skills or not acquire skills. If the worker does acquire skills, the firm then gets to decide whether to compensate the worker or not. The extensive form of the game and the payoffs are below. Which of the following is true? W Acquirre Not Acquire There is no Nash equilibrium. C Compensate Not Compensate This game has a single Nash equilibrium. There are two Nash equilibria. None of the above. (0,0) Both players have a strictly dominant strategy. (10,10) (-5,20)The action set of player 1 is {1,2, 3, 4, 5} (not considering the $ sign). When both players are rational, the theoretical SPNE is (5, 1). Now answer the following problems. What is the dollar equivalent of utility of happiness to ensure player 2 to accept the 2$ offer of player 1? Just write the number, no need to put the $ sign. 5| 5 What is the dollar equivalent of utility of happiness to ensure player 2 to accept the 4$ offer of player 1? Just write the number, no need to put the $ sign. 100 100
- (a) Consider the following games which are commonly used in laboratory exper- iments on social preferences. For each: describe the game, explain how the game would be played by selfish players and summarise the main findings from the experimental evidence. i. Dictator game ii. Ultimatum bargaining game iii. Trust game (b) Carefully comment on the figure below, which shows the percentage of third parties who punish in the dictator game and is taken from Fehr and Fischbacher (2004), "Third party punishment and social norms", Evolution and Human Behavior 25(2).. Percentage of punishers E. Fehr, U. Fischbacher/ Evolution and Human Behavior 25 (2004) 63-87 100 90 80 70 60 50 40 30 20 10 0 A percentage of third parties who punish --percentage of recipients who belief that third parties punish 0 10 20 30 Dictator's transfer to recipient Fig. 1. Percentage of third parties who punished in the dictator game. 40 50 (c) Explain why anonymity of the subjects is an important feature of public good…(a) Consider the following games which are commonly used in laboratory exper- iments on social preferences. For each: describe the game, explain how the game would be played by selfish players and summarise the main findings from the experimental evidence. i. Dictator game ii. Ultimatum bargaining game iii. Trust game (b) Carefully comment on the figure below, which shows the percentage of third parties who punish in the dictator game and is taken from Fehr and Fischbacher (2004), "Third party punishment and social norms", Evolution and Human Behavior 25(2). [10 marks] Percentage of punishers E. Fehr, U. Fischbacher/ Evolution and Human Behavior 25 (2004) 63-87 100 90 80 70 60 50 40 30 20 10 0 A percentage of third parties who punish --percentage of recipients who belief that third parties punish 0 10 20 30 Dictator's transfer to recipient Fig. 1. Percentage of third parties who punished in the dictator game. 40 50 (c) Explain why anonymity of the subjects is an important feature of…Suppose that the University of Alabama and Clemson are making spending decisions for theupcoming year. Assume that Alabama is currently spending $15 million on their recruiting andfacilities, and Clemson is spending $10 million. Each team has an additional $5 million to spendor keep as profits. If they both choose to not spend the additional $5 million then Alabama hasa 60% chance of getting the highest quality quarterback recruit to commit to them (getting thecommitment of the player is the goal). However, if they both choose to spend the additional $5million then there is a 57% chance that Alabama gets the high quality quarterback to commit. IfAlabama spends the additional $5 million but Clemson doesn’t then there is a 67% chanceAlabama gets the recruit. However, if Alabama does NOT spend the additional $5million butClemson does then there is a 50% change either team gets the recruit’s commitment. Setup thepayoff matrix and label the players, their strategies, and their payoffs, and…
- The ultimatum game is a game in economic experiments. The first player (the proposer) receives a sum of money and proposes a fair proposal (F - 5;5) or unfair proposal (U - 8;2). The second player (the responder) chooses to either accept (A) or reject (R) this proposal. If the second player accepts, the money is split according to the proposal. If the second player rejects, neither player receives any money. 1 A 5:5 2 F R 0:0 U A 8:2 2 1. Find the subgame perfect Nash Equilibrium using backward induction. R 0;0Consider the following prisoner's dilemma repeated game with: Samantha of Cooperate Defect on Steve Cooperate 4, 4 -2, 2 Defect 2,-2 0,0 a. Consider two periods of (C,C) followed by one period of (D,C) then (D,D) in the stage game above. What is the discounted utility for both players? b. For what values of the discount factor, is it rational for Player 1 to deviate to D in the first period? Show your work. (You can type in "Delta" to represent 8)3. Consider the ultimatum bargaining game as introduced in the class with the following modification. If the share of player i is x; and that of player j is xj, where j ‡ i, then the payoff of player i is xi - Bxj where > 0. The parameter ß can be interpreted as a measure of envy of player i towards player j. Find the subgame perfect equilibria of this game.