3 Q2GSP vs. VickreyConsider a standard position auction. There are three positions: Top (T), Middle (M) andBottom (B). Position T receives xT = 150 clicks per day, position M receives M = 100 andposition B receives xB = 50 clicks per day. There are five bidders (B1-B5) with the followingdollar values per click: v1 = 12, v2 = 10, v3 = 7, v4 = 5, v5 = 3.(a) Verify whether bidding your value will be an equilibrium of the GSP auction (Google).(b) Find an equilibrium of the GSP auction (Google) with the maximum revenue.(c) Find an equilibrium of the GSP auction (Google) with the minimum revenue.(d) Find the equilibrium of the Vickrey auction (Facebook). Calculate auction revenue.

Second Price Auction Second Price Auction is the auction in which the highest bidder wins the…

Consider a standard position auction. There are three positions: Top (T), Middle (M) and Bottom (B). Position T receives rT = 150 clicks per day, position M receives M = 100 and position B receives rB = 50 clicks per day. There are five bidders (B1-B5) with the following dollar values per click: v1 = 12, v2 = 10, v3 = 7, v4 = 5, v5 = 3. %3D %3D %3D (a) Verify whether bidding your value will be an equilibrium of the GSP auction (Google). (b) Find an equilibrium of the GSP auction (Google) with the maximum revenue. (c) Find an equilibrium of the GSP auction (Google) with the minimum revenue. (d) Find the equilibrium of the Vickrey auction (Facebook). Calculate auction revenue.

Consider a standard position auction. There are three positions: Top (T), Middle (M) and Bottom (B). Position T receives rT = 150 clicks per day, position M receives M = 100 and position B receives rB = 50 clicks per day. There are five bidders (B1-B5) with the following dollar values per click: v1 = 12, v2 = 10, v3 = 7, v4 = 5, v5 = 3. %3D %3D %3D (a) Verify whether bidding your value will be an equilibrium of the GSP auction (Google). (b) Find an equilibrium of the GSP auction (Google) with the maximum revenue. (c) Find an equilibrium of the GSP auction (Google) with the minimum revenue. (d) Find the equilibrium of the Vickrey auction (Facebook). Calculate auction revenue.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter17: Making Decisions With Uncertainty

Section: Chapter Questions

Problem 17.4IP

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You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $40 or $50 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $40 $40 $40 0.125    2 $40 $40 $50 0.125    3 $40 $50 $40 0.125    4 $40 $50 $50 0.125    5 $50 $40 $40 0.125    6 $50 $40 $50 0.125    7 $50 $50 $40 0.125    8 $50 $50 $50 0.125    The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders would not be willing to bid against each…
You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $100 or $125 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) $100 $100 $100 0.125   $100$100$1250.125   $100$125$1000.125   $100$125$1250.125   $125$100$1000.125   $125$100$1250.125   $125$125$1000.125   $125$125$1250.125    The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders would not be willing to bid against each other. The probabilities of the combinations of bidders are still…
1. Individual Problems 18-1 You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $88 $88 $88 0.125    2 $88 $88 $110 0.125    3 $88 $110 $88 0.125    4 $88 $110 $110 0.125    5 $110 $88 $88 0.125    6 $110 $88 $110 0.125    7 $110 $110 $88 0.125    8 $110 $110 $110 0.125    The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders…
True/False a. Consider a strategic game, in which player i has two actions, a and b. Let s−i be some strategy profile of her opponents. If a IS a best response to s−i, then b is NOT a best response to s−i. b. Consider the same game in (a). If a IS NOT a best response to s−i, then a does NOT weakly dominates b. c. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, IS a best response to s−i, SO IS a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. d. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, is NOT a best response to some strategy profile of her opponents, s−i, NEITHER is a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. e. Consider the same game in (a). If a IS a best response to s−i, SO IS any mixed strategy that assigns positive probability to a. f. Consider the same game in (a). If a…
In experiments with randomly assigned private values, the highest average revenue is typically generated by (A) first-price auction; (B) second-price auction; (C) pay-to-bid (bidding fee) auction; (D) English auction.
You are a bidder in an independent private auction, and you value the object at $2000. Each bidder assumes that the valuations are uniformly distributed between $1000 and $5000. Determine your optimal bidding strategy in a first-price sealed bid auction when the total number of bidders are: 2, 10, and 100.
Two identically able agents are competing for a promotion. The promotion is awarded on the basis of output (whomever has the highest output, gets the promotion). Because there are only two workers competing for one prize, the losing prize=0 and the winning prize =P. The output for each agent is equal to his or her effort level times a productivity parameter (d). (i.e. Q2=dE1 , Q2=dE2). If the distribution of “relative luck” is uniform, the probability of winning the promotion for agent 1 will be a function of his effort (E1) and the effort level of Agent 2 (E2). The formula is given by...Prob(win)=0.5 + α(E1-E2), where α is a parameter that reflects uncertainty and errors in measurement. High measurement errors are associated with small values of α (think about this: if there are high measurement errors, then the level of an agent’s effort will have a smaller effect on his/her chances of winning). Using this information, please answer the following questions. Both workers have a…
CPT Inc. is a local manufacturer of conveyor systems. Last year, CPT sold over $2 million worth of conveyor systems that netted the company $100,000 in profits. Raw materials and labor are CPT’s biggest expenses. Spending on structural steel alone amounted to over $500,000, or 25 percent of total sales. In an effort to reduce costs, CPT now uses an online procurement procedure that is best described as a first-price, sealed-bid auction. The bidders in these auctions utilize the steel for a wide variety of purposes, ranging from art to skyscrapers. This suggests that bidders value the steel independently, although it is perceived that bidder valuations are evenly distributed between $4,000 and $21,000. You are the purchasing manager at CPT and are bidding on three tons of six-inch hot-rolled channel steel against 5 other bidders. Your company values the three tons of channel steel at $12,000. What is your optimal bid? Instruction: Enter your response rounded to the nearest penny (two…
CPT Inc. is a local manufacturer of conveyor systems. Last year, CPT sold over $2 million worth of conveyor systems that netted the company $100,000 in profits. Raw materials and labor are CPT’s biggest expenses. Spending on structural steel alone amounted to over $500,000, or 25 percent of total sales. In an effort to reduce costs, CPT now uses an online procurement procedure that is best described as a first-price, sealed-bid auction. The bidders in these auctions utilize the steel for a wide variety of purposes, ranging from art to skyscrapers. This suggests that bidders value the steel independently, although it is perceived that bidder valuations are evenly distributed between $7,000 and $23,000. You are the purchasing manager at CPT and are bidding on three tons of six-inch hot-rolled channel steel against 5 other bidders. Your company values the three tons of channel steel at $12,000. What is your optimal bid?
CPT Inc. is a local manufacturer of conveyor systems. Last year, CPT sold over $2 million worth of conveyor systems that netted the company $100,000 in profits. Raw materials and labor are CPT’s biggest expenses. Spending on structural steel alone amounted to over $500,000, or 25 percent of total sales. In an effort to reduce costs, CPT now uses an online procurement procedure that is best described as a first-price, sealed-bid auction. The bidders in these auctions utilize the steel for a wide variety of purposes, ranging from art to skyscrapers. This suggests that bidders value the steel independently, although it is perceived that bidder valuations are evenly distributed between $8,000 and $25,000. You are the purchasing manager at CPT and are bidding on three tons of six-inch hot-rolled channel steel against four other bidders. Your company values the three tons of channel steel at $16,000. What is your optimal bid?
ollowing is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 8 7 Medium complex, d2 14 5 Large complex, d3 20 -9 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.5 million and as long as the payoff for…
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