Which of the following statements is correct? A social interaction is a strategic interaction where people are aware of the that their actions affect each other. A strategy is an action that a person may take when that person is unaware the effect of their action on others. A best response is the strategy that results in the socially optimal outcome players choose it. A dominant strategy is the strategy that gives the player the highest payoff irrespective of the strategies selected by other players.
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- Describe the Nash equilibrium/a and the mutually-preferred outcome. Finally, consider how people are sometimes able to resolve this social dilemma in the real world. Clearly explain how this method is successful in moving the players to a socially optimal outcome.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.Kayla and Kevin are friends who go together to a used textbook seller who has two copies ofthe biology book that they both need for their class this semester. The cost to the seller ofacquiring the books was $25 each and no other students will need this book. Kayla states thatshe is willing to pay $40 for the book, while Kevin says he is willing to pay $80. Which ofthe following describes the most likely conclusion to this scenario? Group of answer choices The seller will sell the books to both Kayla and Kevin for $40 each because if they tried tocharge Kevin a higher price, Kayla would engage in arbitrage. The seller will sell one book to Kayla for $40 and one book to Kevin for $80 because thismarket meets all three requirements for price discrimination. The seller will sell the books to both Kayla and Kevin for $80 each because Kevin's highervalue exceeds Kayla's willingness to pay. The seller will sell the books to both Kayla and Kevin for $25 each because that is howmuch the…
- Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2. In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid. a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…Describe an original social dilemma you observe in the real world -- i.e. a situation in which no one has an incentive to change what they're doing, but everyone would be better off if everyone changed what they were doing. Try to create two tables to present your dilemma as a 2×2 game. Your first table should be descriptive, Your second table should be a payoff matrix showing the payoffs for both players in each of the four situations Using your payoff matrix, describe the Nash equilibrium and the mutually preferred outcome.There are a kicker and a goalie who confront each other in a penalty kick that willdetermine the outcome of the game. The kicker can kick the ball left or right, while the goaliecan choose to jump left or right. Because of the speed of the kick, the decisions need to bemade simultaneously. If the goalie jumps in the same direction as the kick, then the goalie winsand the kicker loses. If the goalie jumps in the opposite direction of the kick then the kickerwins and the goalie loses. Model this as a strategic form game and write down the matrix thatrepresents the game you modeled. Find the Nash equilibrium.
- In this version of the ultimatum game experiment, one participant is given £100, and is told to offer to split that amount with another participant. The second player can either refuse to accept the division, in which case the participant receiving the £100 has to give it back, or can accept the division, in which case, the player receiving the money splits the £100 as proposed. For the participant who has to accept or reject the offer A) The best strategy is to accept any offer which meets the social norm for fairness. B) The best strategy is to threaten to turn down any transfer of less than £100 to ensure that the person receiving the money makes a fair offer. C) There is a dominant strategy to accept any offer because gaining some money is better than gaining no money D) There is a dominant strategy to turn down any offer other than £50 because an unequal split would be unfair.Consider the following coordination game: Player 2P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game.b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’soutcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarianpreferences.c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as anegative outcome for the individual, ρ = σ = -1. Find the Nashequilibrium(s) with these envious preferences.It is the week before the Yule Ball Dance, and Victor and Ron are each contemplating whether to ask Hermione. As portrayed above, Victor moves first by deciding whether or not to approach Hermione. (Keep in mind that asking a girl to a dance is more frightening than a rogue bludger). If he gets up the gumption to invite her, then Hermione decides whether or not to accept the invitation and go with Victor. After Victor (and possibly Hermione) have acted, Ron decides whether to conquer his case of nerves (perhaps Harry can trick him by making him think he’s drunk Felix Felicis) and finally tell Hermione how he feels about her (and also invite her to the dance). However, note that his information set is such that he doesn’t know what has happened between Victor and Hermione. Ron doesn’t know whether Victor asked Hermione and, if Victor did, whether Hermione accepted. If Ron does invite Hermione and she is not going with Victor— either because Victor didn’t ask, or he did and she…
- Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C. Max prefers A to B to C. Sally prefers B to A to C. To decide which restaurant to go to, the friends adopt the following procedure: First, Max eliminates one of three choices. Then, Sally decides among the two remaining choices. Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining). a.Write down the extensive form (game tree) to represent this game. b.If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be? c.What is the subgame-perfect equilibrium of the above game? d. Does your answer in b. differ from your answer in c.? Explain why or why not. Only typed Answer3.1 Do either of the two telecommunications firms have a dominant strategy in this interaction?If so, what are these dominant strategies? 3.2 What is the Nash Equilibrium of the game above? Clearly, show the logic you use to reachyour conclusion. What type of game is this? 3.3 Suppose the two firms could incentivize or punish each other, could the two firms find theirway to the socially optimum outcome? How would they do this? After observing the strategic interaction between Globogym and Average Joe’s, the governmentdecides to pass a law that states that the two terms must pre-commit to the quantities of trainingsessions they will supply to the American market.Market demand for training sessions is still modeled as ? = 400 − 0.2?, as before, and the marginalcost of production is constant at R40 per call. Let the number of sessions provided by Globogym berepresented by ?G and the quantity provided by Average Joe’s be represented by ?A. 3.4 Solve the firms’ reaction functions and…Rachel, Monica, and Phoebe are roommates; each has 10 hours of free time you could spend cleaning your apartment. You all dislike cleaning, but you all like having a clean apartment: each person’s payoff is the total hours spent (by everyone) cleaning, minus a number 1/2 times the hours spent (individually) cleaning.That is, ui(s1, s2, s3) = s1 + s2 + s3 -1/2si Assume everyone chooses simultaneously how much time to spend cleaning. a. Find the Nash equilibrium. b. Find the Nash if the payoff for each player is: ui(s1, s2, s3) = s1 + s2 + s3 − 3si Is the Nash equilibrium Pareto efficient? If not, can you find an outcome in which everyone is better off than in the Nash equilibrium outcome?