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- QUESTION: What is the Nash equilibrium usineg the payoff matrix below? Profit Payoff Matrix Frontier High Price Frontier Low Price United High Price United 50 Frontier 12 United 40 Frontier 15 United Low Price United 30 Frontier 0 United 25 Frontier 10 A. UNITED: HIGH FRONTIER: HIGH B. UNITED: HIGH FRONTIER: LOW C. UNITED: LOW FRONTIER: HIGH D. UNITED: LOW FRONTIER: LOW E. THERE IS NO NASH EQUILIBRIUM.Two athletes of equal ability are competing for aprize of $10,000. Each is deciding whether to takea dangerous performance-enhancing drug. If oneathlete takes the drug and the other does not, the onewho takes the drug wins the prize. If both or neithertake the drug, they tie and split the prize. Taking thedrug imposes health risks that are equivalent to a lossof X dollars.QuickQuiz Answers1. d 2. c 3. a 4. d 5. c 6. b 7. d 8. ba. Draw a 2×2 payoff matrix describing the decisionsthe athletes face.b. For what X is taking the drug the Nashequilibrium?c. Does making the drug safer (that is, lowering X)make the athletes better or worse off? Explain.Theo and Addy are deciding what toys to pick out at the toy store. Depending on what toys they pick, they can play different games together, but they can’t coordinate their choices. They can’t talk to one another at all until after that make their choice. Below is their payout matrix which shows their utility for each choice. All the bold figures are for Theo and all the non bold figures are for Addy. Addy Strategies Theo Strategies Toy Gas Pump Jump Rope Toy food 20 10 10 3 Ball 7 3 9 4 a) If Theo chooses Toy Food, what would be the possible outcomes for Addy? What would be best for Addy? b) If Addy chose a Toy Gas Pump, what are the possible outcomes for Theo? What would be best for Theo? c) Does Addy have a dominant strategy? If yes, what is her strategy? If not how can you tell? d) Does Theo have a dominant strategy? If yes, what is her strategy? If not how…
- Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.please discuss the separation eqilibrium in details 1. Assume that two players play the Tinder game. There are two types of potential boyfriends: the gentleman (25% of the population) and the douchebag (75% of the population), and they can decide on the different level of effort: low, medium, and high. For the first type, the respective costs are 30, 50, and 80. For the second type, the respective costs are 50, 75, and 120. For the potential boyfriend, the payoff from being in relationship is 130, and the payoff associated with being dumped is 70. The girl can get 60 if she stays single, 100 if she is in relationship with the gentleman, and 25 if she dates the douchebag (credits to Owen Sims) a) Present the game in the extensive form b) Calculate the expected pay-off for the girl. Should she date at all? c) Discuss whether the game has a separating equilibriumConsider a game where each player picks a number from 0 to 60. The guess that is closest to half of the average of the chosen numbers wins a prize. If several people are equally close, then they share the prize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30;(C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization.
- Prisoner's dilemma refers to Question 34Select one: a. how cooperation beween players leads to everyone losing. b. how cooperation can be difficult to maintain, even when all players would win. c. how consumers can maximize their surplus d. how self-interest generates higher profits.Suppose China and the US are deciding whether to join an international agreement to mitigate climate change. The matrix below contains payoffs that represent each country’s net benefit from their decisions. Use this information to answer Question 24. CHINA USA Join Agreement Do Not Join Agreement Join Agreement (100,100) (0,125) Do Not Join Agreement (125,0) (25,25) [24] What does each country decide to do in a Nash equilibrium? AND What is the efficient outcome? Nash: Efficient:Identify a real-world situation in which you see game theory/strategic behavior in action. Explain the game: Who are the players ? What are the strategies they have at their disposal? How are payoffs determined? What, if any, is the Nash equilibrium? Note, this article from Up Journey might help you come up with an example: https://upjourney.com/game-theory-examples-in-real-life
- Imagine that two firms in two different countries want to bring a new product tomarket. Due to economies of scale, if both firms do this, they will both lose £50million. But if only one firm does this, it will gain £300 million.(a) What is the best strategy for firm A, if firm B has not yet entered the market, andwhy?(b) Illustrate this with a game theory diagram, showing appropriate payouts.(c) What is the welfare-maximising strategy for a government, and why?In the movie Rebel Without a Cause, James Dean and Buzz Gunderson compete for thefavours of sixteen year old Judy. Buzz's gang members steal two cars. The group of teenagers gathers on aLos Angeles lookout, with a cliff that drops down to the Pacific Ocean. James and Buzz are to drive the stolencars toward the cliff. The first person to jump from his car is declared the chicken (which is bad). The lastperson to jump is the hero (which is good), capturing Judy's affection and the gang's respect. The driverlesscars continue over the cliff and plunge to the rocks at its base.Each driver can make two possible actions. Jump when he feels endangered (be a chicken) or jump AFTERthe other driver jumps (be a rooster). Assuming that both feel endangered at the same moment, the followingmatrix represents the payoffs for James and Buzz for each choice of strategy.BuzzChicken RoosterJames Chicken 3, 3 -10, 20Rooster 20, -10 -50, -50 PLEASE ANSWER THE BELOW QUESTION WITH REFERECE TO THE ABOVE…The chicken game has often been used to model crises. Recall that in this game, the two players drive straight at each other. They can choose to swerve or keep going straight. If one swerves, and the other goes straight, assume that the one that swerves gets -10 utility and the one that goes straight gets 10 utility, since the one that swerves is deemed the loser. If both swerve, both get 0 utility. If both go straight, they crash and get -50 utility. Assume both players have a discount rate of 0.9 Draw the stage game of date night List all pure strategy Nash equilibria of the single stage game Consider an infinite horizon version of Chicken. Can you get an SPNE in which the both players swerve using a grim trigger type strategy? Consider the following strategies: both players swerve, as long as neither ever went straight. If one player ever plays straight, in all subsequent rounds the player that swerved goes straight and the player that went straight swerves. Can you think…