Two buyers bid in an auction for a single object. Each can bid any integer amount...

Two buyers bid in an auction for a single object. Each can bid any integer amount from $0 to $10. The two bids are made simultaneously and independently of each other. The buyers’ respective values are v1 = 5 and v2 = 10. The bidder with the higher bid wins (obtains the object) and pays the amount of his own bid. However, the bidder who does not win the auction and thus does not get the object is also obliged to pay half of his own bid. In case of a tie in the bids bidder 2 wins.

(a) Specify the best responses to pure strategies for both bidders. (5 points)

(b) Identify the pure strategy NE of the game. (3 points)

(d) Now restrict the possible bids to $4 and $5, and identify all pure and mixed strategy NE in this game. (7 points)

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Two buyers bid in an auction for a single object. Each can bid any integer amount...

Question 6. There are two bidders in a sealed-bid, second-price auction. The object for sale has...

Question 6. There are two bidders in a sealed-bid, second-price auction. The object for sale has a common value. Each bidder, i = 1,2, receives a signal i that is independently and uniformly distributed on the interval [0, 1]. The true value of the object, v, is the average of the two signals, v = (σ1 + σ2) / 2 (a) If bidder 1 gets the signal σ = 0.7, how much does he think the object is worth? (b)...

There is single object to be sold to one of the n potential buyers. Each buyer...

There is single object to be sold to one of the n potential buyers. Each buyer has a valuation of vi for the object. Consider the auction rule where the winner is the highest bidder, and pays the minimum of all the bids, i.e. min{bi : i ∈ N}. In this game, truthtelling is a dominant strategy equilibrium. Is it true or false ?

Suppose a single good is being sold in a sealed-bid auction (no bidder can observe the...

Suppose a single good is being sold in a sealed-bid auction (no bidder can observe the bids of other bidders). The rules of the auction are such that the person who bids the highest value for the good wins, but the winner only has to pay the value of the second-highest bid submitted. Assume that there are three people bidding for the good (?=1,2,3), and each values the good according to: ?1=$12 ?2=$16 ?3=$3 where ??v_i is the maximum willingness...

A seller wishes to auction a single unit of an indivisible object. She can do so...

A seller wishes to auction a single unit of an indivisible object. She can do so in one of the following two ways (i) through a first-price auction to n bidders, (ii) through a second-price auction with optimally chosen reserve price to n - 1 bidders. Each bidder's valuation is private information and is an independent draw from the uniform distribution on [0, 1]. The seller values the object at 0. (a) Which of the two alternatives would you recommend...

Two players compete in an auction to win an object. Players’ valuation for the object are...

Two players compete in an auction to win an object. Players’ valuation for the object are different: player i’s value for winning the object is vi , for i = 1, 2, with v1 > v2 > 0. These values are publicly known. The rules of the auction are the following: (a) Each player submits a bid bi ∈ [0,∞) to the auctioneer. (b) The player who makes the highest bid wins the object and pays the auctioneer bi ....

There are two players in the game. Each player can pick any integer number between 1...

There are two players in the game. Each player can pick any integer number between 1 and n. If two numbers are the same then player 1 pays 1 dollar to player 2. If two numbers are different than nothing happens. (a) Prove that there are no equilibria in pure strategies; (b) Prove that in the equilibrium each strategy should be played with a positive probability. (c) Find all NE of the game.

Consider a sealed-bid auction in which the winning bidder pays the average of the two highest...

Consider a sealed-bid auction in which the winning bidder pays the average of the two highest bids. As in the auction models considered in class, assume that players have valuations v1 > v2 > ... > vn, that ties are won by the tied player with the highest valuation, and that each player’s valuation is common knowledge. Is there any Nash equilibrium in which the two highest bids are different? If there is, give an example. If there is not,...

Game theory: Analyze the second price" auction. There are two bidders and one object being sold...

Game theory: Analyze the second price" auction. There are two bidders and one object being sold by auction. Each bidder knows what the object is worth to him, but not what it is worth to the other bidder. In other words, the object is worth v1 to bidder 1 and v2 to bidder 2. Bidder 1 knows v1 but not v2, while bidder 2 knows v2 but not v1. In the sealed bid second price auction, each bidder privately submits...

Consider a two-person problem in which there is a single seller who owns an indivisible object and single potential buyer of the object Each agent has a value for the object that is known to him but not known to the other agent.

Consider a two-person problem in which there is a single seller who owns an indivisible object and single potential buyer of the object Each agent has a value for the object that is known to him but not known to the other agent. The mechanism for (possible) trade is that each agent announces a price, and if the buyer's announcement is larger than the seller's announcement, the object is sold to the buyer at the seller's announced price. There is...

Subjects