[Auctions and Reserve Prices] Consider a seller who must sell a single private valuegood. There are two potential buyers, each with a valuation that can take on one of threevalues, vi E {0,1,2}, each value occurring with an equal probability of 1/3. The players' valuesare independently drawn.The seller will offer the good using a second-price sealed-bid auction, but he can set a reserveprice of r≥ 0 that modifies the rules of the auction as follows. As seen in class, if both bids arebelow r, then neither bidder obtains the good and it goes "poof"! If both bids are at or above rthen the regular auction rules prevail. If only one bid is at or above r then that bidder with thehighest bid obtains the good and pays r to the seller.a. What is the expected revenue of the seller when r = 0 (i.e., no reserve price)?b. Is it still a weakly dominant strategy for each player to bid his valuation when r >0? What is the expected revenue of the seller when r = 1?c. What is the optimal reserve price r for the seller, and what is the optimalexpected revenue of the seller? (You may assume r is an integer.)

To find optimal price of the seller, we need to maximise the expected revenue

Answered: [Auctions and Reserve Prices] Consider…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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