Consider a second price auction with 2 bidders, 1 and 2, who have values for the...

Consider a second price auction with 2 bidders, 1 and 2, who have values for the good of 20 and 80, respectively. Each knows what the other bidder’s valuation is so there is no uncertainty.

(a) Show that choosing a bid equal to one’s valuation is a weakly dominant strategy for bidder 1.

(b) Show that if each bidder plays a weakly dominant strategy, the bidder with the highest value always wins the good

(c) Is it a Nash equilibrium for bidder 1 to bid 60 and bidder 2 to bid 80? Which bidder is playing a weakly dominated strategy?

Expert Solution

Rahul Sunny answered 2 years ago

Consider a second price auction for a single item with two bidders. Suppose the bidders have...

Consider a second price auction for a single item with two bidders. Suppose the bidders have independent private values, uniformly drawn in the interval [0, 1]. Suppose the seller sets a reserve price p = 0.5; that is, only bids above p = 0.5 can win. If a bidder bids above p and the other bids below p, then the first bidder wins and pays a price p. If both bid above p, then the highest bidder wins and pays...

Consider a private value auction with 2 bidders. The auction is carried out as a second...

Consider a private value auction with 2 bidders. The auction is carried out as a second price sealed bid auction where in case of a tie between the bidders, the winner is selected by a coin toss. The seller has valuation of the good of zero and will accept any bid at or greater than zero. Each bidder knows his/her own valuation, v, and does not know the valuation of the other bidder. It is common knowledge that the bidder...

Consider 45 risk-neutral bidders who are participating in a second-price, sealed-bid auction. It is commonly known...

Consider 45 risk-neutral bidders who are participating in a second-price, sealed-bid auction. It is commonly known that bidders have independent private values. Based on this information, we know the optimal bidding strategy for each bidder is to: A. bid their own valuation of the item. B. shade their bid to just below their own valuation. C. bid according to the following bid function: b = v − (v − L)/n. D. bid one penny above their own valuation to ensure...

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...

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)...

Auction Auction Price Age of Item Number Bidders 1 $946 113 9 2 $1,336 126 10...

Auction Auction Price Age of Item Number Bidders 1 $946 113 9 2 $1,336 126 10 3 $744 115 7 4 $1,979 182 11 5 $1,522 150 9 6 $1,235 127 13 7 $1,483 159 9 8 $1,152 117 13 9 $1,545 175 8 10 $1,262 168 7 11 $845 127 7 12 $1,055 108 14 13 $1,253 132 10 14 $1,297 137 9 15 $1,147 137 8 16 $1,080 115 12 17 $1,550 182 8 18 $1,047 156 6...

Consider a second-price sealed-bid auction. Suppose bidders' valuations are v1=10 and v2=10. Select all that apply....

Consider a second-price sealed-bid auction. Suppose bidders' valuations are v1=10 and v2=10. Select all that apply. (PLEASE EXPLAIN CHOICES COMPLETEY) a. One bidder submitting a bid equal to 10 and the other submitting a bid equal to 0 is a Nash equilibrium. b. Bidding a value b1 equal to her own valuation v1 is a weakly dominated strategy for bidder 1. c. Both bidders submitting bids equal to 0 is a Nash equilibrium. d. Both bidders submitting bids equal to...

We consider a GSP auction with four bidders, A, B, C and D. Since there are...

We consider a GSP auction with four bidders, A, B, C and D. Since there are four bidders only the three highest bidders will be displayed). The click frequency of the first, second and third positions are 100 clicks/hour, 75 clicks/hour and 35 clicks/hour, respectively. Bidders’valuation per click are vA = 10, vB = 6, vC = 4, vD = 3. Bidder B, C and D bid 5, 3 and 1, respectively. What is the optimal bid for A?

Consider a 2-person private value, first-price auction. The object is worth $10,000 to bidder 1 who...

Consider a 2-person private value, first-price auction. The object is worth $10,000 to bidder 1 who knows that bidder 2’s value is uniformly distributed between 0 and $40,000. Assume that bidder 2 is going to use his equilibrium bidding strategy. a) What is bidder 1’s optimal bid for his value $10,000 and what is his expected payoff? b) Assume that bidder 1 learns that the object is worth $22,000 to bidder 2 and in turn, bidder 2 is not aware...

Question 3 Jo and Jim are bidding in a second-price, independent, private value auction. Their values...

Question 3 Jo and Jim are bidding in a second-price, independent, private value auction. Their values for the object are independently and uniformly distributed on the interval (1,2). (1) What is the expected value of the winning bidder? (2) What is the expected value of the price?

Question