Suppose Jack and Jill are bidding in a first price auction. Jack and Jill's valuations are drawn from a uniform distribution between $[0,10]$. Jack's valuation is 5.2 and Jill's valuation is 4.8.
a. What are their equilibrium bids?
Jack bids 4.89 and Jill bids 4.52 .
c. Are your answers to (a) and (b) different? Why? What happens to their equilibrium bid functions as the number of bidders goes to $\infty$ ?
As the number of bidders goes to infinity, then $\frac{n-1}{n} \rightarrow 1$ and Jack and Jill bid their valuation.

Question

Suppose Jack and Jill are bidding in a first price auction. Jack and Jill's valuations are drawn from a uniform distribution between $[0,10]$. Jack's valuation is 5.2 and Jill's valuation is 4.8.
a. What are their equilibrium bids?
 Jack bids 4.89 and Jill bids 4.52 .
c. Are your answers to (a) and (b) different? Why? What happens to their equilibrium bid functions as the number of bidders goes to $\infty$ ?
 As the number of bidders goes to infinity, then $\frac{n-1}{n} \rightarrow 1$ and Jack and Jill bid their valuation.

Quizplus · Accepted Answer

The Answer of Suppose Jack and Jill are bidding in a first price auction. Jack and Jill's valuations are drawn from a uniform distribution between $[0,10]$. Jack's valuation is 5.2 and Jill's valuation is 4.8.
a. What are their equilibrium bids?
 Jack bids 4.89 and Jill bids 4.52 .
c. Are your answers to (a) and (b) different? Why? What happens to their equilibrium bid functions as the number of bidders goes to $\infty$ ?
 As the number of bidders goes to infinity, then $\frac{n-1}{n} \rightarrow 1$ and Jack and Jill bid their valuation.

Suppose Jack and Jill Are Bidding in a First Price [0,10][0,10][0,10]

Suppose Jack and Jill Are Bidding in a First Price $[0,10]$