(a) Argue that the strategy profile in which each buyer bids according to the function B defined by B(v) = v/2 is not a Nash equilib- rium. Hint: Find a profitable deviation for some v € [0, 1]. (b) Suppose the seller uses a posted price p. What is her expected revenue? Which price maximizes her expected revenue? Hint: What is the probability of at least one buyer is willing to pay p? (c) Recall that in the first price auction, the seller's expected revenue is (n-1)/(n+1). Compare the seller's revenue from the first-price auction and that from posted-price selling.

(a) Argue that the strategy profile in which each buyer bids according to the function B defined by B(v) = v/2 is not a Nash equilib- rium. Hint: Find a profitable deviation for some v € [0, 1]. (b) Suppose the seller uses a posted price p. What is her expected revenue? Which price maximizes her expected revenue? Hint: What is the probability of at least one buyer is willing to pay p? (c) Recall that in the first price auction, the seller's expected revenue is (n-1)/(n+1). Compare the seller's revenue from the first-price auction and that from posted-price selling.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.6P

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