The Mathematics of ... Auctions (via a&l daily) Going Once, Going Twice By the time an auctioneer shouts "Sold!" most bidders have already gone too far The phenomenon that bidders in auctions pay too much can be seen at Ebay every day. The irrational behaviour of bidders is probably an important reason for Ebay's success. Another striking example were the state-organised UMTS auctions in Europe for the new mobile telephone technology networks where many companies paid much more than they will ever get back from future clients. The Nash equilibrium which implies that there is only one optimal strategy in a competitive game assumes rational participants knowing that their opponents are rational as well and cannot explain this. A new approach by the economist Thomas Palfrey called quantal response equilibrium takes into account that people are risk averse in the sense that they prefer to bid too much to losing the item altogether. The last paragraph of the article illustrates the problem of predicting what the other bidders think strikingly: "Even the most rational people can be predictably irrational, Palfrey concludes. In some business schools, professors make an exercise of auctioning off a dollar to their students, stipulating that both top bidders will have to pay. The best strategy is simply not to bid, Palfrey says. 'But then it's tricky, because if everyone else realizes this, then why don't I bid 10 cents? It would be irrational for anybody else to bid 11 cents. Well, the problem is that some clown out there is going to bid 11 cents.' Once the bidding gets going, he says, often only the professor can stop it." Further reading: The 29 page scientific paper Quantal Response Equilibrium and Overbidding in Private-Value Auctions for the geeks. Could the exaggerations (in both directions) at the stock market also be explained using this theory? In a bull market stock prices usually go up too much and in a bear market they go down too much. The efficient market hypothesis which states that all the information available now is in the current prices never convinced me. Not only that it is tautological and does not really explain anything, it also does not take into account misinformation and irrational behaviour which is very common. There definitely is an irrational hysterical element here as well. People don't want to miss the boat when prices go up (men are greedy) and hop on the train when prices are already too high and they sell their stocks when prices fall so that prices fall even more and even more people sell. The stop-loss limits which are nowadays carried out by computers even enforce this phenomenon. I have to dig deeper into this.