uestion 1 /hich of the following is correct? the prisoners' dilemma game, the equilibrium is ometimes socially optimal. ne lab experiments of the public goods game how that people are not solely self-interested. the lab experiments of the ultimatum game, ffers by the proposer are never rejected by the esponder because something is better than othing. ne ultimatum game is a simultaneous game.
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- 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.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?Refer to the Ultimatum Game in Figure 17.7. Recall that the payoffs are monetary payoffs. a. Suppose that players only care about monetary payoffs, with $1 = 1 util. Find the subgame– perfect equilibrium. b. Suppose that players are imperfectly altruistic. They receive 1 util for each dollar they earn but = util for each dollar the other player earns.Write down the extensive form reflecting the new payoffs. Find the subgame–perfect equilibrium. c. Suppose that players are perfectly altruistic, receiving 1 util for each dollar in the sum of their earnings. Write down the extensive form reflecting the new payoffs. Find the subgame– perfect equilibrium. d. Suppose that players are perfectly selfless, getting 1 util for each dollar the other player earns but no utility for their own earnings. Write down the extensive form reflecting the newpayoffs. Find the subgame–perfect equilibrium. Does player 1 end up choosing the outcome that player 2 prefers?…
- For the operating system game, let us assume Windows is more superior than Mac intrinsically and that network effects are stronger for Macs. These modifications are reflected in different payoffs. Now, the payoffs from adopting Windows is 30 + 10 × w and from adopting Mac is 20 × m. n consumers are simultaneously deciding between Windows and Mac, where n > 10. (a) Is there a Nash equilibrium in which everyone buys Windows? Explain your answer. (b) Is there a Nash equilibrium in which everyone buys Mac? Explain your answer. (c) Is there a Nash equilibrium in which some consumers buy Windows and some consumers buy Mac? Explain your answer.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…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.
- 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 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.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…
- Let us see the example of Juan and María given but modify their preferences. It is still the case that they are competitive and are deciding whether to show up at their mom’s house at 8:00 A.M., 9:00 A.M., 10:00 A.M., or 11:00 A.M. But now they don’t mind waking up early. Assume that the payoff is 1 if he or she shows up before the other sibling, it is 0 if he or she shows up after the other sibling, and it is 1 if they show up at the same time. The time of the morning does not matter. Find all Nash equilibria.1) What are the Nash equilibria? Which one is unreasonable/non-credible threat? 2) What are the subgame perfect Nash equilibria? Does SPNE concept eliminate the unreasonable Nash equilibrium?Suppose Justine and Sarah are playing the ultimatum game. Justine is the proposer, has $140 to allocate, and Sarah can accept or reject the offer. Based on repeated experiments of the ultimatum game, what combination of payouts to Justine and Sarah is most likely to occur?.