EBK MICROECONOMICS
2nd Edition
ISBN: 8220103679701
Author: List
Publisher: YUZU
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Question
Chapter 17, Problem 2Q
To determine
The ways in which a sealed bidding differs from open-outcry auctions.
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Use the expected value information to illustrate how having more bidders in an oral auction will likely result in a higher winning bid.
How to solve this question?
Consider an antique auction where bidders have independent private values. There are two bidders, each of whom perceives that valuations are uniformly distributed between $100 and $1,000. One of the bidders is Sue, who knows her own valuation is $200. What is Sue's optimal bidding strategy in a Dutch auction?
A famous local baker has approached you with a problem. She is only able to make one wedding cake each day and 5 people have requested a wedding cake on the same day. Rather than pick randomly which person she will sell the cake to, she decides to have an auction.
Is this auction more representative of a private value or common value auction? Why?
Which auction method(s) do you recommend the baker choose to maximize the amount of money she can make, and why?
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- Consider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.arrow_forwardHello, please help me to solve this question in Game Theory. Thanks in advance!Consider a first price sealed-bid auction of an object with two bidders. Each bidder i’s valuation of the object is vi, which is known to both bidders. The auction rules are that each player submits a bid in a sealed envelope. The envelopes are then opened, and the bidder who has submitted the highest bid gets the object and pays the auctioneer the amount of his bid. If the bidders submit the same bid, each gets the object with probability 0.5. Bids must be integers. Find a Nash equilibrium for this game and show whether it is unique.arrow_forwardConsider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. Compute the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.arrow_forward
- “While auctions are appealing in theory, the challenges of auction design in practice are insurmountable” discussarrow_forwardConsider a game where there is a $2,520 prize if a player correctly guesses the outcome of a fair 7-sided die roll.Cindy will only play this game if there is a nonnegative expected value, even with the risk of losing the payment amount.What is the most Cindy would be willing to pay?arrow_forwardExplain why a player in a sealed-bid, second-price auction would never submit a bid that exceeds his or her true value of the object being sold. (Hint: What if all players submitted bids greater than their valuations of the object?)arrow_forward
- See attachments for question context. Question: Some people advocated the following modifiction of the auction rule. A bidder cannot bid for only one object, i.e., if at some point in time he withdraws from the bidding race for one object, he automatically withdraws the race for the other object. Every other aspect of the auction, including how prices increase over time, does not change. What should a bidder do if his valuation for the two objects are 50 and 60, respectively? Explain. Does the auction lead to an efficient allocation? Explain.arrow_forwardConsider the following situation: five individuals are participating in an auction for an old bicycle used by a famous cyclist. The table below provides the bidders' valuations of the cycle. The auctioneer starts the bid at an offer price far above the bidders' values and lowers the price in increments until one of the bidders accepts the offer. Bidder Value ($) Roberto 750 Claudia 700 Mario 650 Bradley 600 Michelle 550 What is the optimal strategy of each player in this case? Who will win the auction if each bidder places his or her optimal bid? If Claudia wins the auction, how much surplus will she earn?arrow_forwardConsider two bidders – Alice and Bob who are bidding for a second-hand car. Each of them knows the private value she/he assigns to the car, but does not know the exact value of others. It is common knowledge that the value of other bidders is randomly drawn from a uniform distribution between 0 and $10000. Assume that Alice values the car at $8500 and Bob values the car at $4500. a) If Alice and Bob participated in the second-price sealed bid auction, what would they bid and what would be the result of the auction? Explain your answer. b) If they participate instead in a first-price sealed bid auction, what would they bid and what would be the result of the auction? Explain your answer. c) Calculate and compare the revenue of the seller in the above situations. Which type of auction should the seller use? Explain your answerarrow_forward
- Consider a first-price, sealed-bid auction, and suppose there are only three feasible bids: A bidder can bid 1, 2, or 3. The payoff to a losing bidder is zero. The payoff to a winning bidder equals his valuation minus the price paid (which, by the rules of the auction, is his bid). What is private information to a bidder is how much the item is worth to him; hence, a bidder’s type is his valuation. Assume that there are only two valuations, which we’ll denote L and H, where H > 3 > L > 2. Assume also that each bidder has probability .75 of having a high valuation, H. The Bayesian game is then structured as follows: First, Nature chooses the two bidders’ valuations. Second, each bidder learns his valuation, but does not learn the valuation of the other bidder. Third, the two bidders simultaneously submit bids. A strategy for a bidder is a pair of actions: what to bid when he has a high valuation and what to bid when he has a low valuation. a. Derive the conditions on H and L…arrow_forwardAt a company, 20 employees are making contributions for a retirement gift.Each person is choosing how many dollars to contribute from the interval[0,10]. The payoff to person i is bi X xi - xi, where bi > 0 is the “warm glow”he receives from each dollar he contributes, and he incurs a personal cost of 1.a. Assume bi < 1 for all i. Find all Nash equilibria. How much is collected?b. Assume bi > 1 for all i. Find all Nash equilibria. How much is collected?c. Assume bi = 1 for all i. Find all Nash equilibria. How much is collected?Now suppose the manager of these 20 employees has announced that shewill contribute d > 0 dollars for each dollar that an employee contributes.The warm glow effect to employee i from contributing a dollar is now bi X(1 + d) because each dollar contributed actually results in a total contribution of 1 + d. Assume bi = 0.1 for i = 1, . . . , 5; bi = 0.2 for i = 6, . . . , 10; bi = 0.25 for i = 11, . . . , 15; and bi = 0.5 for i = 16, . . . , 20.d. What…arrow_forwardCommon pool resource game) Consider a common pool resource game with two appropriators. (If you don’t know what is a common pool resource, read the Wikipedia article about the ”Tragedy of the Commons”.) Each appropriator has an endowment e > 0 that can be invested in an outside activity with marginal payoff c > 0 or into the common pool resource. Let x ∈ X ⊆ [0, e] denote the player’s investment into the common pool resource (likewise, y denotes the opponent’s investment). The return from investment into the common pool resource is x x+y · ((x + y) − (x + y) 2 ). So the symmetric payoff function is given by π(x, y) = c · (e − x) + x x+y · ((x + y) − (x + y) 2 ) if x > 0 and c · e otherwise. Assume 1 − e < c < 1. Find Nash equilibrium of the game. Proceed by deriving the best response correspondences first. How does Nash equilibrium depend on parameters c and e (varying one at a time and keeping the others fixed)?arrow_forward
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