Question: Consider the independent private value auction model where there are 2 bidders and each bidder's valuation, Vi, is uniformly distributed on [0, 1], for i

Consider the independent private value auction model where there are 2 bidders and each bidder's valuation, Vi, is uniformly distributed on [0, 1], for i = 1, 2. That is, the distribution function of both V1 and V2 is F(v) = v for v [0,1].

(a) In the first price auction, show that it is a Nash equilibrium for each bidder to bid Bi(v) = B(1)(v) = 21v, for i = 1,2.

(b) Suppose the seller sells the product by posted price, instead. For any price p [0, 1] the seller sets, what is the expected revenue of the seller? What is the p that maximizes his expected revenue?

(c) Compare his maximized revenue from posted-price selling with his ex- pected revenue from the first price auction, 1/3. Can you think of a reason why the seller wants to sell the good through first price auction, even if it may mean lower expected revenue than posted-price selling?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Economics Questions!

The Thomas Company is in the process of developing a revolutionary new product. A new division of the company was formed to develop, manufacture, and market this product. As of yearend (December 31,...

1. (3 points) We want to analyze an all-pay auction. For this consider an auction environment with 2 bidders and independent private values. Values v; are distributed uniformly on [0,1]. Players...

Consider the following first-price, sealed bid, private value auction of an object to two bidders. In the auction, the highest bidder wins the bid and pays her bid. Suppose that for i = 1, 2, bidder...

Consider the private value auction model, with n bidders. Each bidder's value is drawn independently from U[0,100]. (a) Suppose the seller runs a second-price auction. What is the expected selling...

Hi, this has to do with auctions and mechanism design! In a first-price, all-pay auction, the bidders simultaneously submit sealedbids. The highest bid wins the object and every bidder pays the...

Problem 2 ( A Second Price Auction with an Optimally Chosen Reserve Price ) . Two bid - ders, indexed by i = 1 , 2 , compete for an item, which the seller does not value. Each bidder i s valuation vi...

4. (20 points) Consider the auction model with a continuum of possible valuations. Bidder i's valuation, Vi, is drawn from the uniform distri- bution on [0, 1], for i = 1, 2, ..., n. In other words,...

4. (20 points) Consider the auction model with a continuum of possible valuations. Bidder i's valuation, Vi, is drawn from the uniform distri- bution on (0,1), for i = 1,2, ..., n. In other words,...

1. The sell side is composed of: a. Mutual funds b. Hedge funds c. Pension funds d. Online Brokers e. All of the above f. Only a. and b. g. Only a., b., and c. 2 In the US, the SEC regulates trading...

Do Qs 4 only. The model is the same as Qs 2 as mentioned in the qs hence why i have included qs 2 as well. 2. (20 points) Consider the two-bidder auction example in class, where 4. (20 points)...

1 COS n 1 Cos n +1 Find the sum of the series > if it is convergent. n=1

From Pozar, ex. 8.3: Design a maximally flat low-pass filter with a cutoff frequency of 2 GHz, impedance of 50 Ohm (i.e. Rs-RL= 50 Ohm), and at least 15 dB insertion loss at 3 GHz. Compute and plot...

It wrong 5:28 63 Take Quiz Exit Incorrect Question 4 0 / 1 pts E C Price level, P B D ADI ADo AD 2 Output, Y Figure 10.1 Refer to Figure 10.1. Suppose that the economy were at point A, and the...

A 35.0 mL solution of a Co2+ with concentration 0.20 M is titrated with a 0.10 M EDTA solution buffered at pH=9. Find the pCo2+ after adding the following volumes of titrant: a)Vadded- 20.0 mL,...

A substance has an enthalpy of vaporization of 22.89 kJ mol1. If the vapor pressure is 0.153 bar at 14.83 C, what is the temperature when the vapor pressure is 1.000 bar?

The following purchases of widgets by Loopy Company took place during the 1st Quarter of 2019: Date 01/20/2019 02/15/2019 03/12/2019 If the only product Loopy sold during the first quarter was...

Suppose a new mosquito-borne virus has emerged and has caused 550 cases to- date. The number of cases worldwide is doubling exponentially every 5 months. Assuming continuous growth, what is the...

-) Explain the six domino principles

1. What information of vital importance is not expressed in the message? The answer to the question tells us a little about the code used between the parties.

2. Find five metaphors for communication.

5. Starting with a motive you may have for acting the way you do in a particular situation: a) What purpose did you seek to achieve? b) Which aspects of your past and your surroundings influenced...