You are a bidder in an independent private values auction, and you value the object at $4,000. Each bidder perceives that valuations are uniformly distributed between $1,500 and $9,000. Determine your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:

a. 2 bidders $2,750

b. 10 bidders $3,750

c. 100 bidders $3,975

Explanation:

Calculation to determine what your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:

Using this formula

Optimal bidding = Bidder's own valuation - (Bidder's own valuation - Lowest valuation) ÷ Number of bidders

Let plug in the formula

a) 2 bidders

Optimal bid = $4,000 - [($4,000 - $1,500) ÷ 2]

Optimal bid = $4,000 - ($2,500÷2)

Optimal bid = $4,000 - $1,250

Optimal bid = $2,750

b) 10 bidders

Optimal bid = $4,000 - ($4,000 - $1,500) ÷ 10

Optimal bid = $4,000 - ($2,500÷10)

Optimal bid = $4,000 -$250

Optimal bid =$3,750

c) 100 bidders

Optimal bid = $4,000 - ($4,000 - $1,500) ÷ 100

Optimal bid = $4,000 - ($2,500÷100)

Optimal bid = $4,000-$25

Optimal bid = $3,975

Therefore your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:

a. 2 bidders $2,750

b. 10 bidders $3,750

c. 100 bidders $3,975