Two friends, Albert (A) and Berta (B), have to decide on going to one- of three bars, Xenia's (X), Yara's (Y), or Zana's (Z). They decide to select a bar by alternatively vetoing bars until one remains. First Albert vetoes a bar. If at least two bars remain, then Berta vetoes another bar. That process continues until a single bar remains unvetoed. Suppose Albert prefers Xenia's to Yara's to Zana's and Berta prefers Zana's to Yara's to Xenia's. Assume that, for each of the two, going to their most preferred bar gives a utility of 2, going to their next preferred bar gives a utility of 1, and going to their least preferred bar gives a utility of 0. Model this as an extensive form game and find its Nash equilibria. Which of the Nash equilibria are subgame perfect?
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- 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…you and a friend decide to run a three mile race. If you agree to run together, you keep up with himfor the first mile, but you overexert yourself and run the last two miles at slower paces on your own. Tomake up for lost time, your friend runs the last two miles at a faster pace. Your mile times are 6:30, 7:00,and 7:30. Your friend’s times are 6:30, 6:00, and 6:00. If you both agree to run on your own, you run aconstant pace of 7:05 while your friend runs at a constant pace of 6:05. If you want to run together butyour friend wants to run solo, he runs his constant pace of 6:05. You, on the other hand, want to showhim that you can run faster, but you end up overexerting yourself after the first mile. You run times of6:20, 7:05, and 7:30. If he wants to run together but you do not, you both run at your pace of 7:05. Thissituation can be turned into an economic game, with the payoffs the overall race times. You each wantto run the fastest time you possibly can.(a) Who are the players in…A game is played as follows: First Player 1 decides (Y or N) whether or not to play.If she chooses N, the game ends. If she chooses Y, then Player 2 decides (Y or N) whetheror not to play. If he chooses N the game ends. If he chooses Y, then they go ahead and playanother game with the payoffs shown below. A player who opts out by choosing N gets 2 andthe other player gets 0. Draw the tree of this game and then find the two subgame-perfect Nashequilibria.
- GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.learn.canterbury.ac.nz Clasarsom Nov 15-ICO EUC LEARN | AKO See the game below and answer the questions 8 to 11: Player-1 C Player-2 X, Y Y Player-1 9 14 8. Player-2 16 17 16 Nash Equilibrium in this game: Select one: O a. Playert: C; Player2: X O b. Playert: C; Player2: Y Oc. Playert: L; Player2: X Od. Playert: L; Player2: Y e. NoneA6. 1.Adam and Zoey are competing fish and chips sellers in Linear City. They are located at the twoopposing ends of the town’s 3-mile-long Main Street. The 1700 inhabitants of the town are distributeduniformly on Main Street and each of them eats at most one portion of fish and chips for lunch. People’sdisutility from getting to a fish and chips stand and back home amounts to $2 for each mile of distanceto the stand. The marginal cost of producing one portion of fish and chips is $9. The consumers areuniformly distributed along the street. Each consumer has a valuation of $29.0 for the product. Supposethat both Zoey and Adam can advertise at zero cost to inform everyone about their business. Find theequilibrium price of Zoey if neither of the two sellers advertises.
- Game Theory Question A non-profit firm is on a local community online donation platform for a community event it wants to hold (only community members can donate via the website). The event will be held only if the non-profit firm collects $20,000 total from members of the community. Each member values the event at $500. Suppose that there are 100 community members. Community members can only donate by purchasing a lottery ticket from the firm. Each ticket costs $200 and only one ticket can be purchased per member. The proceeds will be collected by the firm. The lottery winner gets a premier meal at a local restaurant that's worth $100. Remember, the firm keeps all the donated money. If the amount of donations is less than $20,000, then the firm returns the donated money to the community members (since there'll be no event held but the lottery winner still gets to eat that fancy meal). If the donations sum up to $20,000, the community event will take place. What are the Nash…N=2 video broadcasting websites, You and Twi, must decide the number of minutes of ads to be displayed for every video that the user elects to watch. Let tY be the number of ad-minutes per video set by You, and tT the number of ad-minutes per video set by Twi. Streaming one video costs You cY=0.02, while it costs Twi cT=0.03. There are 100 million potential users, and each watches videos according to the following demand curves: qY((tY,tT) =10-2tY+tT=10-2tT+tY a- What is the cross-price elasticity between You and Twi? b- Suppose, for now, that You and Twi enter an (illegal) agreement by which they set tY=tT=t Derive the total number of users in the market as a function of t. Derive the profits for each website as a function of t. c- Now let the two platforms compete by each setting their number of ad-minutes: i. What is the best reply of You? What is the best reply of Twi? ii. Find the Nash Equilibrium of the game. iii. How many total users choose You and how many total users choose…There are 2 players. They take Ston eS From the Pilt of 6 Stones. Player 1 can takt only 2 or 3 Stones. piayer 2 can taKeS only 2 or 4 StonesS. P layers take turns, observe dil Previous moves, and player 1 mover first. A pla yer loses if She can not make a legal move, While another player ir declared the Winner. Let the pay oF OF Winning egval to 1 and the payoFF OF losing equal to 0. a) represent the in ɛxtemsive Form (depict Only legalmoes) b) Find all SPNE OF this game& explain your a mwwer. Who Will Win ? game Only legalmar)
- Two firms, A and B, are each considering trying to develop a newwidget. Whichever firm is first to develop the new widget wins a patent worth $20 million plus a penny.Developing a new widget involves several ‘steps’. The firms alternate moves, with A moving first, until oneof them wins the patent. All moves are observed. In each turn, a firm can choose whether to take 0, 1, or2 development ‘steps’. Taking 0 steps in a turn costs that firm $0. Taking 1 step in a turn costs $4 million.And taking 2 steps in a turn costs $11 million. For simplicity, assume a zero discount rate. Initially, eachfirm is 4 steps away from completing development.(a) Describe and explain carefully what will happen in this patent race and why. [Hint: it may help toread Dutta ch 12 (but notice I changed the numbers).](b) Very briefly explain what is the economic rationale for granting ‘intellectual property rights’ such aspatents. What are some disadvantages for society of granting such rights?While grading a final exam, an economics professordiscovers that two students have virtually identical answers.She is convinced the two cheated but cannot prove it. The professorspeaks with each student separately and offers the followingdeal: Sign a statement admitting to cheating. If both studentssign the statement, each will receive an “F” for the course. Ifonly one signs, he is allowed to withdraw from the course whilethe other student is expelled. If neither signs, both receive a “C”because the professor does not have sufficient evidence to provecheating.a. Draw the payoff matrix.b. Which outcome do you expect? Why?Two politicians from the same party decide whether to support or oppose the gov- ernment's environmental policy. Politician A prefers that they both support, but Politician B prefers that they both oppose. Both politicians agree that the party should have a coherent position and the worst outcome is that one supports and the other opposes the policy. (a) Formulate this situation as a strategic game - specify the players, actions, and payoffs (you can set-up a table of the actions and payoffs). (b) What are the Nash equilibria of this game? Explain your answer.