1. You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions.
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- You are playing a game with a friend. It’s yourmove but you don’t have a dominant strategy.Your payoff depends on what your friend doesafter your move. You consider flipping a coin todecide what to do. You are about to reach for acoin, but then you realize that your friend has adominant strategy. Explain how using backwardinduction (rather than a coin toss) will now determine your next movelearn.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. NoneExercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?
- 1. Arif and Aisha agree to meet for a date at a local dance club next week. In their enthusiasm, they forget to agree which venue will be the site of their meeting. Luckily the town has only two dancing venues, Palms and Oasis. Having discussed their tastes in dancing venues last week, both know that Arif prefers Palms to the Oasis and Aisha prefers the Oasis to Palms. In fact, their payoffs reflect that if both go to Oasis, Aisha's utility is 3 and Arif's 2, while if both go to Palms Arif's utility is 3 and Aisha's is 2. If they do not go to the same venue, then they both have a utility of 0. Write the payoff matrix and explain whether there are any pure Nash equilibria. Carefully explain what these are and why. Comment on the existence of any dominant strategy equilibria. Please calculate mixed strategy equilibria, if any, and then derive the probability that Arif and Aisha will find themselves at the same venue. Carefully explain the steps to your solution;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…
- You need to paint your fence but you really hate thistask. You decide to hire the kid next door to do it foryou. You would be willing to pay him up to $100,but you start by offering $50, expecting to negotiate. To your great surprise, he accepts your $50 offer.When you tell your friend about the great deal yougot, she is shocked that you would take advantage ofsomeone. What can you tell your friend to assure herthat you did not cheat the kid next door?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…3. Suppose that the various Balls of basketball or internet fame Lavar, Lamelo, Liangelo, Lonzo,and Spalding are considering playing in a 1-on-1 tournament. They get a payoff of 0 if theydecide not to participate. The following table illustrates their payoffs across the variousscenarios. 1 Player 2 Players 3 Players 4 Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 10 9 8 7 6 a. Find and describe all pure strategy Nash Equilibria.b. Suppose now Spalding, since it is in fact a literal basketball, gets a payoff of 0 in anycircumstance, being an inanimate object. The table is now as follows: 1 Player 2 Players 3 Players 4Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 0 0 0 0 0 Find and describe all pure strategy Nash Equilibria.
- 4. Sonia the Terrible lands her ship and crew of scurvy-pirate raiders onto a foreign beach. Up on the headland is a village, led by Jen the Brave. At this point, Sonia has a choice: she can SLASH her water barrels, eliminating her water supplies; or she can NOT SLASH, which keeps her water supplies completely intact. Having seen the action taken by Sonia, Jen can choose to CHARGE or to WAIT. The payoffs are as follows: if Sonia the Terrible chooses to SLASH and Jen CHARGES, the payoffs are (100, 20) to Sonia and Jen, respectively. If Sonia SLASHES and Jen WAITS, the payoffs are (10, 30). On the other hand, if Sonia chooses to NOT SLASH and Jen CHARGES, the payoff is (20, 15). If Sonia opts to NOT SLASH and Jen chooses to WAIT, the payoffs are (40, 10), respectively. What is the subgame perfect (or credible) equilibrium outcome? a. Sonia the Terrible chooses to SLASH; Jen the Brave chooses to CHARGE b. Sonia the Terrible chooses to NOT SLASH; Jen the Brave chooses to WAIT c. Sonia the…1. Consider the following sequential game: Left (3,5) Mary Go (6,4) Up Right John Stop (5.7) John (a) Draw the game tree of the game. John Go Down (4,1) Left Mary Stop (2,5) Right (6,-1) (John as player 1 and Mary as player 2) By backward induction, find a Nash equilibrium and the corresponding payoffs. 2. Eve and Noa start with $10 in each of their piles. They take turns choosing one of two actions, continue or stop, with Eve choosing first. Each time a player says continue, $10 will be removed from her pile, and $20 will be added to the other player's pile. The game automatically stops when the total amount in their piles reaches $60. (Eve as player 1 and Noa as player 2) (b) By backward induction, find a Nash equilibrium and the corresponding payoffs.2.19. Standard setting. Suppose Apple and Samsung are in the process of negotiating a common standard for a new 3D camera tech- nology they plan to introduce in the next generation of smartphones. Apple has a preference for standard A, whereas Samsung has a pref- erence for standard S. However, both recognize that multiple stan- dards are a worse outcome for all. Specifically, Apple gets 240 if it selects A and Samsung does so too, but only 20 if Samsung does not adopt A. If Apple adopts standard S and Samsung does so too, then Apple gets a payoff of 190. If, however, Samsung chooses A then Ap- ple gets zero. For Samsung, the situation looks similar: If Samsung chooses standard S and Apple does the same then Samsung gets 210, but if Apple chooses A the Samsung's payoff is only 30. If Samsung opts for standard A and Apple does so too then Samsung gets a pay- off of 110, whereas if Apple chooses standard S then Samsung gets a payoff of zero. (a) Suppose that both Apple and Samsung…