Answered: (a) Argue that the strategy profile in…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Transcribed Image Text:1. " valuations. Bidder i's valuation, Vi, is drawn from the uniform distri- bution on [0, 1], for i = 1,2, ..., n. In other words, the cdf of Vi, can be defined as F(v) = v for v E [0, 1] (and, of course, F(v) = 0 for v < 0 and F(v) = 1 for v > 1). Each bidder's valuation is independent of any other bidder's valuation. Consider the first-price auction. As I have ar- gued in class, the strategy profile in which B;(v) = B(v) = (n– 1)/n·V for all v e [0, 1] and i = 1, 2, ...,n is a Nash equilibrium. For this ex- ercise, consider the case n = 3. Consider the auction model with a continuum of possible (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 E [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.

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