2. Consider a first-price sealed-bid auction with known valuations. There is one object for saleand there are two bidders. The bidders' valuations are commonly known: One bidder hasvaluation 5 for the object. The other bidder has valuation 10 for the object.The rules of the auction are as follows: The bidders submit bids simultaneously and indepen-dently. Only integer bids are permitted, i.e., allowable bids are 0, 1, 2, ..with the highest bid is equally likely to be declared the winner (standard tie breaking). Thewinner gets the object and pays her bid.Each of the bidders(a) Find each bidder's best reply function.(b) Find all Nash equilibria.(c) Are any of the Nash equilibria strict?

Two Players 1 & 2 FOR PLAYER 1 Let the bids of player 1 be (b1) b1 has 5 valuations Actual…

Answered: 2. Consider a first-price sealed-bid…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Equilibria in an auction Suppose a single item will be sold to one of two bidders. Each bidder's value is drawn uniformly at random from the interval [0, 1]. Each bidder will simultaneously name a price and the item will be sold to the higher bidder for the price that bidder named. If this price is p and the winning bidder has a value of v then the utility of the winning bidder is v-p and the utility of the losing bidder is 0. This situation is more complex than the normal form games we studied in class for two reasons. First, the set of strategies is infinite. Second, rather than known utilities there is uncertainty over them, so we need a Bayesian model and in general the equilibrium strategy will depend on (i.e. be a function of) v. This assignment walks you through the derivation of an equilibrium in this setting. (a) Suppose your value is v and the bid of the other bidder is uniformly distributed on [0,0.5]. If you bid p, what is your expected utility? (b) Suppose your value is…
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(The All-Pay Auction). The seller has an item for sale. The valuations of the bidders are independently and identically distributed on R+ with a c.d.f. F. Find the symmetric equilibrium of an auction with two bidders in which both bidders pay their own bids but only the highest bidder wins the object. Show that each bidder’s expected payment is the same in this auction and in the first-price auction.
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Two rival companies competing in the same market need to decide their plans for future expansion of their stores. The Table below shows the possible outcomes of their mutually interdependent actions (payoffs are profits in £m) Giga Company Titanic Conglomerate No Change Refurbishment of existing stores Large Expansion No Change 30, 40 25, 35 15, 24 Refurbishment of existing stores 35, 30 28, 32 18, 33 Large Expansion 12, 22 18, 20 20, 25 The Nash equilibrium: (A) does not exist. (B) occurs when both firms choose Refurbishment of existing stores. (C) occurs when both firms choose Large Expansion. (D) occurs when both firms choose No Change.
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You have three tickets to a Celtics game on a night that you are going to be out of town (so the value of unsold tickets is zero to you). There are only four possible buyers of a Celtics ticket. The table below lists the respective reservation prices of these four possible buyers: Customer Reservation Price 1 $25 2 $35 3 $50 4 $60 a) How much revenue can you generate using the English auction mechanism from the sale of the first ticket? [Bids can be made in increments of $1.00] b) How much revenue can you generate using the English auction mechanism from the sale of the second ticket? [Bids can be made in increments of $1.00] c) How much revenue can you generate using the English auction mechanism from the sale of the third ticket? [Bids can be made in increments of $1.00] d) How much total revenue can you generate using the English…
Question 6 A collector of rare antique books wants to sell a book from her collection on eBay. Discuss the following decisions, considering the characteristics of the item for sale and the anticipated market for this item: (a) When offering the book in a regular auction, what should the start price of the auction be? (b) When offering the book at a fixed posted price, would the optimal posted price be above or below the optimal start price of an auction in part (a)? (c) Should the item be offered in a regular auction or at a fixed posted price?

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