Q&A: Second-Price Auction in Game Theory
Second-Price Auction in Game Theory
Question
I read an article about economics and game theory and came across the following paragraph:
"I happened to walk into a lecture on game theory, and the lecturer gave an example of a beautiful model called a second-price auction," she says. "In a second-price auction, all the participants are told: submit in a sealed envelope the maximum price you are willing to pay, but in practice you will pay the second-highest price that was offered. That way, they have nothing to lose by offering their true value. Suppose someone offered 100 and the second price was 80, then they will pay only 80 and enjoy the difference anyway. If they offer less than the second price, they will lose the product. Therefore it is worthwhile for them to offer the price the product is truly worth to them. Studies show that this is a method that incentivizes people to tell the truth."
I think this does not necessarily incentivize people to offer the price the product is worth to them, because if it is important to them to buy the product, then they will not want to risk offering a price lower than second place. Maybe two people will offer above their own valuation and win the auction?
Am I missing something? Could you help me understand?
Answer
I immediately looked for an article or lecture by my friend Michal Feldman on this topic. I found that this is where you took the quote from (she is the speaker): https://www.globes.co.il/news/article.aspx?did=1001496727
First of all, as far as I know, the thesis of the "second-price auction" has been confirmed in empirical studies, meaning that people really are incentivized in this way to tell the truth. Even so, one can still ask why.
The assumption is that each person makes decisions on their own. Therefore, they offer a price based on their own decision and not in coordination with anyone else. When you think about it on your own, you make the calculation she describes there: if I offer more than I am willing to pay, that could hurt me because I might win. If I offer less than what someone else offers, I will not win. Therefore I offer what it is truly worth my paying.
It seems to me that you are assuming that he wants to win the product at any price, and ignoring the fact that he also does not want it at too high a price.
Discussion on Answer
That is indeed proven. This is basically how auctions on eBay work, with great success. Anyone who has participated in eBay auctions knows that this is no small psychological trick on the bidder. Inexperienced participants may even bid more than they were originally willing to pay, because they do not think that others too will bid more than what seems to them to be the item's value, and they want to guarantee themselves the win. Usually, products are sold above the price offered in "buy it now," and once the bidding passes the immediate-purchase price, that option is canceled. If an item has quite a few bids and still has a buy-it-now option, then if the price is good, it is recommended to buy it immediately. This auction method is brilliant.
Indeed, you are right; I assumed that it was important to him to win the product even at a high price. Most people will buy at a price that is worth it to them, as empirical research shows.
Until now we have been referring to the price that people are willing to pay. But what about the product's "true" value (or the value the seller perceives it to have)? It is possible that the bids will be very far from it.