Question

4. You are a bidder in an independent private values auction, and you value the object at $3,500. Each bidder perceives that valuations are uniformly distributed between $500 and $7,000. Determine your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:

a. 2 bidders.

Bid: $


b. 10 bidders.

Bid: $


c. 100 bidders.

Bid: $

Answer 1

In a first price, sealed-bid auction with independent private valuation, the optimal strategy for a bidder is to bid less than his evaluation of the item.

In case of uniformly distributed evaluations, the said optimal bid = bidder's own valuation-[(bidder's own valuation-Lowest valuation)/number of bidders].

a.) Using the above formula in case there are 2 bidders, optimal bid equals $2,000

b.) Using the above formula in case there are 10 bidders, optimal bid equals $3,200

b.) Using the above formula in case there are 100 bidders, optimal bid equals $3,470

In other words, higher the number of bidders, higher the optimal bid.