EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
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Question
Chapter 15, Problem 15.7P
a
To determine
Equilibrium bidding strategies and seller’s expected.
b)
To determine
Equilibrium bidding strategies and seller’s expected revenue if there are three bidders and N bidders
c)
To determine
Sellers expected revenue from a first price, second bid auction.
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Students have asked these similar questions
Discrete All-Pay Auction: In Section 6.1.4 we introduced a version of an all-
pay auction that worked as follows: Each bidder submits a bid. The highest
bidder gets the good, but all bidders pay their bids. Consider an auction in
which player 1 values the item at 3 while player 2 values the item at 5. Each
player can bid either 0, 1, or 2. If player i bids more than player j then i wins
the good and both pay. If both players bid the same amount then a coin is
tossed to determine who gets the good, but again both pay.
a. Write down the game in matrix form. Which strategies survive IESDS?
b. Find the Nash equilibria for this game.
David wants to auction a painting, and there are two potential buyers. The value for eachbuyer is either 0 or 10, each value equally likely. Suppose he offers to sell the object for $6, and the two buyers simultaneously accept or reject. If exactly one buyer accepts, the object sold to that person for $6. If both accept, the object is allocated randomly to the buyers, also for $6. If neither accepts, the object is allocated randomly to the bidders for $0.
(a) Identify the type space and strategy space for each buyer.
(b) Show that there is an equilibrium in which buyers with value 10 always accept.
(c) Show that there is an equilibrium in which buyers with value 10 always reject.
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…
Chapter 15 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
Ch. 15.2 - Prob. 1TTACh. 15.2 - Prob. 2TTACh. 15.2 - Prob. 1MQCh. 15.2 - Prob. 1.1MQCh. 15.2 - Prob. 2.1MQCh. 15.2 - Prob. 1.1TTACh. 15.2 - Prob. 2.1TTACh. 15.2 - Prob. 1.2TTACh. 15.2 - Prob. 2.2TTACh. 15.3 - Prob. 1MQ
Ch. 15.3 - Prob. 2MQCh. 15.4 - Prob. 1MQCh. 15.4 - Prob. 1.1MQCh. 15.4 - Prob. 2.1MQCh. 15.5 - Prob. 1TTACh. 15.5 - Prob. 2TTACh. 15.5 - Prob. 1MQCh. 15.5 - Prob. 2MQCh. 15 - Prob. 1RQCh. 15 - Prob. 2RQCh. 15 - Prob. 3RQCh. 15 - Prob. 4RQCh. 15 - Prob. 5RQCh. 15 - Prob. 6RQCh. 15 - Prob. 7RQCh. 15 - Prob. 8RQCh. 15 - Prob. 9RQCh. 15 - Prob. 10RQCh. 15 - Prob. 15.1PCh. 15 - Prob. 15.2PCh. 15 - Prob. 15.3PCh. 15 - Prob. 15.4PCh. 15 - Prob. 15.5PCh. 15 - Prob. 15.6PCh. 15 - Prob. 15.7PCh. 15 - Prob. 15.8PCh. 15 - Prob. 15.9PCh. 15 - Prob. 15.10P
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