The Hindu Business Line : Auctions, with twists in the tail

Sothebys, the auction major, was in town. This time around it was auctioning things other than art objects. Among others, there would be fiction and non-fiction books as well. Wafers, the young CA, loved books more than she loved movies and the myriad things that women of her age desired. She decided to go for the auction but was not sure how to bid. And so she called on the encyclopaedic China to gather some inputs.

“The strategy would depend on what kind of auction Sotheby is making,” said China. “Now what would that mean?” asked Wafers, clearly stumped. “After all, an auction is an auction. The highest bidder takes home the product.”

China disagreed. “Well not exactly. There is another form of auction popular on Internet sites where you win if you bid the highest but the price you pay is what the second highest bidder had bid for.”

Watching Wafers’ half-blank look, China decided to supply some numbers. “What you had indicated is called the first price auction. What I named is called the second price auction.

In a first price auction, the person who bids the highest gets the product at the price at which he bid. Suppose, Debbie, Reuben and Sheetal bid for a product. Suppose they bid Rs 400, Rs 350 and Rs 300 respectively. Debbie gets the product by paying Rs 400.”

Second Price Winner

Wafers cottoned on. She didn’t want to get dismissed as a muff. She said, “And in the case of the second price auction, for the same bidding, Debbie gets the product but by paying Reuben’s price, namely Rs 350.” China was suitably impressed. “You like the second price auction more than the first price auction?” he asked.

“Yeah,” said Wafers. “I love it because it generates Consumer’s Surplus.” She remembered the phrase from her PE-1 days.

Her economics professor had explained it with an earthy example. “You notice a product which you want to buy. Mentally you think it would cost you Rs 200. The shopkeeper tells that the price is Rs 150.”

The professor had then asked, “What would you do?” And the class had screamed, “We would buy,” the class had screamed. The professor matching scream for scream wondered aloud, “But why?” And the class had responded in chorus, “Because we would save Rs 50.” The professor closed out saying that this Rs 50 represented the consumer’s surplus; the difference between what you want to pay and what you actually end up paying.

“Your analogy of a second price auction with the consumer’s surplus is right only up to a point. There is a twist in the tail of which I will come to later,” said China, clearly holding the upper hand in this conversation.

“I wouldn’t know whether Sotheby is the first price auction or the second price auction,” remarked Wafers. “What I do know is that these would be closed-bid not open-bid auction, meaning that you will have to give out your bid in a sealed paper and cannot bid a second time.” China smiled. “Would the strategies be different?” asked Wafers.

Different Strategies

“Yeah, in a first price auction, you should always bid less than what the product is worth for you. Suppose you want to bid for table tennis bat whose worth in your view is Rs 500. If you bid Rs 500 and win then you gain nothing. If you bid Rs 400 and win, you gain Rs 100. The lower you bid the greater is the benefit from winning. On the flip side the lower you bid, the lower is the chance that you will win,” said China.

Wafers was impatient. “So what should I do?” China again smiled. “Basically you will have to second-guess what others will bid for and accordingly pitch your bid”.

Wafers sighed. She had looked for a step by step procedure of the kind she had learnt in her CA classes but China hadn’t offered her any of that.

“What do I do if it is second price option?” she asked, hoping that there would be some formula to fall back upon. “Bid the full value of the product” said China almost instantly. “What” screamed Wafers? China decided to explain.

“Suppose in your view the table tennis bat is worth Rs 500. You can bid either above Rs 500 or below Rs 500. If you bid above Rs 500, say, Rs 550 you win the auction if no one bids above Rs 550. If someone has bid above Rs 500 but less than Rs 550 (say, Rs 530) you win the auction but end up buying the bat at a price which is above what you felt was the right value. In this case you end up buying at Rs 530.”

“It’s like operation successful, patient dead?” asked Wafers. China nodded and internally made note of the point that Wafers, post her CA, was becoming quick on the uptake.

“But what if someone had bid less than Rs 500, say, Rs 490?” asked Wafers. China replied, “In that case you would have still won the auction if you had bid Rs 500! So there was no point bidding Rs 550; there is no point in bidding above Rs 500. So the upper bid limit for you is Rs 500.”

Why shouldn’t I bid less than Rs 500, say, Rs 475?

“In that case if someone bid between Rs 475 and Rs 500, he wins the auction. If someone had bid less than Rs 475, say, Rs 460 you win the auction and pay Rs 460. Well you would have still got the bat at Rs 460 by bidding Rs 500. So there is no point in bidding less than Rs 500!”

“In short” said Wafers, pushing her hair backwards, “in a second price auction you should instantly quote the maximum price that you are willing to pay, namely, the fair price of the product.”

China closed out with his favourite word, “Precisely.”

Racy@TheHindu.co.in

http://Racycases.blogspot.com

More Stories on : Insight | Racy Cases

Article E-Mail :: Comment :: Syndication :: Printer Friendly Page

Stories in this Section
Auctions, with twists in the tail

Leave the rupee to the market

Is the housing sector too unorganised to offer reliable statistics?

Just Do IT

Number Crunch

Don’t let the downs in life deter you

From crisis to consensus