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Results from the Vickery (second price) and first price auctions Nash Equilibrium Predictions--What you should have done to make the most money! (rational choice) Why don't any of us have a "beautiful mind" all the time? Some answers from evolutionary psychology.
Professor Schulze Lecture 2 AEM 414 Results Of Vickery Auction: Most Bids Equal Value AEM 414 Professor Schulze Lecture 2 Results of Vickery Auction: Demand Curve AEM 414 Professor Schulze Lecture 2 Results of First Price Auction: Most Bids Below Value AEM 414 Professor Schulze Lecture 2 Results of First Price Auction: Demand Curve AEM 414 Professor Schulze Lecture 2 Distribution Of Earnings By Auction Type With Same ` Earning Potential In Each -Participants are endowed with $10 per round for each of 20 rounds, for a total baseline wealth of $200 -Distributed between the two auction types, then, subject total baseline wealth for the Vickery auctions is $100, and the total baseline wealth for the First-Price auctions is $100 -1 participant made money in the 2nd price auction/ 25 lost money/ 35 broke even. -13 participant made money in the 1st price auction/ 24 lost money/ 24 broke even. AEM 414 Professor Schulze Lecture 2 Nash Equilibrium Both Provides The Best Strategy And Predicts Results For 1st And 2nd Price Auctions In game theory, the Nash equilibrium (named after John Nash) for games involving two or more players exists when each player plays the optimal strategy, where no player has anything to gain by changing only one's own strategy. If there is a set of strategies for a game with the property that no player can benefit by changing his strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute a Nash equilibrium.
Lecture 2 AEM 414 Professor Schulze Vickery 2nd Price Auction: Intuition The high (winning) bidder pays a price equal to the second highest bid. The logic below shows she should bid her value: If she bids more, say $10 when her value is $6, if the price (2nd highest bid) is $9 she loses $3. By winning when she shouldn't, she shouldn' loses. If she bids less, say $2 when her value is $6, if the price is $3 (2nd highest bid) she fails to earn $3 which she would have with a winning bid of $6. By losing when she should have won, she loses. William Vickrey (Columbia) figured this out and won the Nobel Prize in 1996 and died 3 days later.
Lecture 2 AEM 414 Professor Schulze Vickery 2nd Price Auction: Nash Equilibrium AEM 414 Professor Schulze Lecture 2 Psychologists, however, might make the following predictions: Note that the English (in class) and Vickrey (in lab) Auctions are theoretically the same! Both use the second price. You might reason incorrectly. In the Vickrey, it is easy to think: "Since I do not pay what I bid, I will just put in a high bid to increase my odds of winning." Oops. Vickrey bids may be high! Many people put in $10 bids, their entire balance! However, in the English Auction (remember, the winner is the last person standing and pays the price at which the next to last person sat down, the 2nd price), as the price sweeps upwards, as in class, it is very easy to see that you should get out before the price exceeds your value so you do not lose money. The English auction is transparent in this regard and should prevent over-bidding. AEM 414 Professor Schulze Lecture 2 The English and Vickrey Auctions Although they seem different, both are second price auctions. Understanding what to do, bid an amount equal to your induced value, can be learned two ways according to psychologists. First, there is the "aha" phenomenon. This is what economic theory thinks always happens--you analytically figure out the optimal strategy. The alternative to reasoning is learning. Thus, you try something out, see if it works, and then try to do something else to see if it works better. Most importantly, in the English Auction the optimal strategy is more transparent. The "aha" is easier to get than in the Vickrey Auction. Generally, sealed bid, simultaneous auctions are harder to understand than sequential auctions.
AEM 414 Professor Schulze Lecture 2 First Price Auction: Intuition High bid wins and winner pays own bid. To make any money you have to bid less than value. But, the lower you bid, the lower the odds of winning. The higher you bid, the higher your odds of winning. The more bidders, the harder it is to make money-more competition. Intuition is pretty good!
Professor Schulze Lecture 2 AEM 414 First Price Auction: Nash Equilibrium XXXXX 1-1/N AEM 414 Professor Schulze Lecture 2 Comparing Predictions Prediction from economics: Vickrey Bid = English Bid = Value > First Price Bid Predictions from psychology and economics: Vickrey Bid > English Bid = Value > First Price Bid Note predictions from behavioral economics and psychology are about adding systematic errors to rational choice theory. Overbidding in the Vickrey Auction is a natural mistake. Both English and First Price Auctions are Transparent.
Professor Schulze Lecture 2 AEM 414 Why? An answer from evolutionary psychology. The social sciences (business, economics, sociology, and psychology) traditionally have viewed the mind as a blank slate. This empty hard drive was filled with an operating system, software, and memories by parents, schools, and culture. Human behavior was the product of this programming and data entry. In contrast, biologists and evolutionary psychologists believe that the mind was evolved to solve very specific problems encountered by our ancestors. The mind consists of a number of evolved problem solving modules. These modules may or may not be adequate to solve the problems that culture, technology, and the economy now present. Intuition often fails. This course focuses on systematic errors that occur when intuition fails. An analytical approach is then required.
Professor Schulze Lecture 2 AEM 414 ...
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This note was uploaded on 02/20/2009 for the course AEM 4140 taught by Professor Schulze,w. during the Fall '08 term at Cornell University (Engineering School).
- Fall '08