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Two neighboring homeowners, i = 1,2, simultaneously choose how many hours to spend maintaining a lawn. The AVERAGE benefit per hour for i is
(e.g., it is for homeowner 1)
And the (opportunity) cost per hour for each homeowner is 4.
(a) Give each homeowner’s (net) payoff as a function of and .
(b) Compute the Nash equilibrium.
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- Demonstrate the concept of coordination failure by using the payoff matrix and prove that, Coordination failure among economic agents can lead to an inefficient outcome while the opposite can guide to an efficient outcome. Use any hypothetical scenario to justify your analysis.Problem 4 A person has been mugged in the street by a thief, and there are n witnesses. All of the witnesses prefer someone else to chase the thief but none of them want to be the person trying to catch her. Each person gets 0 utility if the crime goes unreported, v if the crime is reported by someone else, and v −c if they report the crime. Moreover, we assume that the cost of chasing the thief is less than the utility of catching the thief: c < v. a. Define the strategic game described above. b. Find players’ best responses. c. Find the Nash equilibria of the game.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?
- An old lady is looking for help crossing the street. Only one person is needed to help her; if more people help her, this is no better. You and I are the two people in the vicinity who can help; we have to choose simultaneously whether to do so. Each of us will get pleasure worth a 3 from her success (no matter who helps her), But each one who goes to help will bear a cost of 1, this being the value of our time taken up in helping. If neither player helps, the payoff for each player is zero. Set up this game in strategic form.Your total benefits from spending time with your spouse are shown in the following table. Hours per Day Total Benefit 0 0 1 20 2 38 3 54 4 68 5 80 6 90 7 98 8 104 Alternatively, you have the option of working as many hours as you want, earning $11 per hour. Assume this is the next best use of your time. Use the marginal principle to find your optimal number of hours to spend with your spouse per day. The optimal amount of time for you to spend with your spouse is hours per day Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Suppose that a decision maker faced with four decisions alternatives and four state of nature developing the following profit payoff table: Outcomes Alternatives S1 S2 S3 S4 A1 14 9 10 5 A2 11 10 8 7 A3 9 10 10 11 A4 8 10 11 13 Use Maximax, Maximin, Criterion of realism (? = 0.55, and ? = 0.4), Laplace, and Minimax regret to find the best alternative.
- Suppose an emissions standard is implemented that required each plant to reduce its pollution by 5,000 tons. What will be the Total Cost of Pollution Reduction for the entire industry? Suppose instead of an emissions standard, the government implements a tradeable permit system. Each firm is now given 3,000 permit each (1 permit equals 1 ton of pollution allowed). How many permits will be traded between the 2 firms? (Hint: The total amount that need to be reduced is 10,000 tons. i.e. Q1 + Q2 = 10,000)On the basis of Table 1.1, you may infer that the law of increasing opportunity costs applies to increasing production ofA) Stealth bombers but not to B-1 bombers.B) B-1 bombers.C) Both B-1 bombers and Stealth Bombers.D) Neither B-1 bombers or Stealth Bombers.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…
- When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .There are two firms, whose production activity consumes some of the clean air that surrounds our planet. The total amount of clean air is K > 0, and any consumption of clean air comes out of this common resource. If firm i ∈ {1, 2} uses ki of clean air for its production, the remaining amount of clean air is K − k1 − k2. Each player derives utility from using ki for production and from the remainder of clean air. The payoff of firm i is given by ui(ki , kj ) = ln(ki) + ln(K − ki − kj ) j ≠ i ∈ {1, 2}. (a) Assuming that each firm chooses ki ∈ (0, K), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs?Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They consume both good X, a private good, and the protection from the fort, P. One unit of good X costs 1 unit while one unit of P costs 2 units, so the budget constraint for each is given by: Xi + 2Pi = 100. Both Jon and David have an income of 100 and a utility function of the form: U = log(Xi) + 2log(Pj + Pd) (a) How much protection, P, will be privately provided? What is optimal consumption of X, the private good? (b) What are the socially optimal amounts of protection, P, and consumption, X, of the private good? How do the socially optimal amounts compare to that privately provided? Explain why.