If two art dealers bidding for a Picasso receive the following forecast information about the chance of a forgery which with previously unknown Picasso paintings is present 8 times in 10 historically,what is the amount by which strategic underbidding could be reduced if ten bidders were attracted to the auction?

Question

If two art dealers bidding for a Picasso receive the following forecast information about the chance of a forgery which with previously unknown Picasso paintings is present 8 times in 10 historically,what is the amount by which strategic underbidding could be reduced if ten bidders were attracted to the auction?
If two art dealers bidding for a Picasso receive the following forecast information about the chance of a forgery which with previously unknown Picasso paintings is present 8 times in 10 historically,what is the amount by which strategic underbidding could be reduced if ten bidders were attracted to the auction?

Quizplus · Accepted Answer

The Answer is With two bidders the optimal amount of strategic underbidding is 1/n-th (50%)if the bidders have private values based on different distribution channels or different complementary resources or different tastes of a private client.With ten bidders the proportion of underbidding would fall to 10%.Hence,40% of the winning bidder's private value would be lost to the seller who conducts a two-bidder auction.

The Bayesian probability information should be seen as a further basis for reduction of all bids.

With two bidders the optimal amount of strategic underbidding is 1/n-th (50%)if the bidders have private values based on different distribution channels or different complementary resources or different tastes of a private client.With ten bidders the proportion of underbidding would fall to 10%.Hence,40% of the winning bidder's private value would be lost to the seller who conducts a two-bidder auction. The Bayesian probability information should be seen as a further basis for reduction of all bids. Therefore,the winning bidder would pay only 0.36 of his willingness to pay (up from 0.2 before receiving the forecast)and this amount would be further reduced by 10% (to 0.324 of X)with ten bidders and by 50% (to 0.18 of X)with two bidders.Hence the seller's expected revenue from attracting ten bidders rather than two increases by 0.324X - 0.18X = 0.144X,by fourteen percent.

Therefore,the winning bidder would pay only 0.36 of his willingness to pay (up from 0.2 before receiving the forecast)and this amount would be further reduced by 10% (to 0.324 of X)with ten bidders and by 50% (to 0.18 of X)with two bidders.Hence the seller's expected revenue from attracting ten bidders rather than two increases by 0.324X - 0.18X = 0.144X,by fourteen percent.

If Two Art Dealers Bidding for a Picasso Receive the Following