Keywords: auction Poisson process stop rules
Auction has a long history and its origin is very early. According to records, in Babylon, Central Asia in 500 BC, men got their wives by auction. Auction was also very popular in ancient Rome. People sell trophies, goods, real estate and even the throne through auction. The form and history of auction are recorded in detail in Casady's book (1967), but it is a pity that this book is not easy to read in China. Throughout the ages, the items being auctioned are also varied, from antique calligraphy and painting to daily necessities, from agricultural products to seafood, national debt, business licenses, and various tangible and intangible items with radio frequency have been reported. In recent years, auction has been used to sell government assets, telecom licenses and products in the electricity market, which has attracted people's attention. On the other hand, with the development of Internet and e-commerce, online auction is also booming. Not only have professional auction websites appeared, but many transactions are also conducted through auctions.
Auction theory is a branch of economics that has developed rapidly in recent twenty years. Vickery, the founder of modern auction theory from 65438 to 0996, won the Nobel Prize in Economics, which is an important symbol. The origin of auction method is very early, but the recorded theoretical research began in 1950s and 1960s. Vickery put forward a formal auction model and got the famous "principle of income equivalence". Vickery's model is a private value model. Soon after, Wilson put forward the common value model, and all kinds of auction research appeared in various management magazines. In 1980s, the research of auction theory also made new and important progress. Reliey, Samuelson (198 1) and Myerson (198 1) also proved a more general "principle of income equivalence": in any two auction models with different private values, if the goods are always obtained by the person with the highest evaluation, the income of the person with the lowest evaluation is. Moreover, Myerson( 198 1) also proved the conditions that the general optimal auction mechanism should meet. At the same time, Milgrom and Weber (1982) put forward the "attached value" model, which unified the models of private value and public value and provided a new framework for the study of auction theory.
The principle of income equivalence has become the benchmark for the development of auction theory, and the subsequent theoretical progress lies in relaxing the hypothetical conditions of the hypothetical principle. The conditions of income equivalence are: (1) participants are risk neutral. Auctioneers and bidders are risk-neutral. (2) auction only one item. (3) The evaluation of auction items by different bidders is an independent private evaluation, which is not influenced by others' evaluation. (4) There is no collusion between bidders. (5) The bidders are symmetrical, their evaluations have the same distribution, and they have the same information about the auction structure. At the same time, the literature puts forward four standard auction modes: English auction, dutch auction, first price auction and second price auction. One of them is. The first two auctions are public auctions, and the last two auctions are sealed price auctions. When studying all the conditions of relaxing the principle of reciprocity of income, we often compare the income of four standard auctions, and come to the conclusion that sometimes the British auction is the best, and sometimes the first price is the best. The mechanism design of auction has an important influence, and there is no universal optimal auction method. On the one hand, with the government issuing telecom licenses, power control and privatization of public utilities by auction in the 1990s, the realistic economic phenomenon has raised new problems to the auction theory. On the other hand, with the development of theory, the research of auction theory has broken through the research of single item auction, and discussed the problem of simultaneous auction of multiple unit products. The early research mainly focused on the benefits of various auction forms, and gradually shifted to the discussion of the most efficient auction: that is, the auction result is that the bidder with the highest evaluation of the item gets the auction item. This reflects that in the auction sponsored by the government, efficiency is the key to consideration, and it is a remarkable example of combining theory with practice.
Not only does the government attach importance to auction, but with the development of e-commerce and online transactions, the development of online auction also puts forward requirements for theory. In the study of optimal auction theory, the number of auction participants is fixed. From the perspective of mechanism design, auction is a set of rules, which determines the reward of the winner and all participants in the auction. The number of participants in the general optimal auction mechanism proved by myerson (198 1) is fixed. In the auction of important items, there is usually a period of preparation time, in order to spread the news of the auction and attract enough bidders to make the auction go smoothly. However, in the network environment, the auction participants can change, and the auction participants are affected by the number of people browsing the auction web page, which can be considered as a random variable, so this factor should be considered in the auction design. For this situation, we can use the following examples to illustrate. Suppose you have a walkman. The current trend is to listen to various styles of MP3 players. You want to join the trend, but you don't have enough cash. At this time, you want to sell the walkman. You often surf the Internet and know that online auctions are very popular, so you want to auction them off. You need money, you want to sell the walkman as soon as possible, but you also want to sell it at a good price. When you start the auction, you don't know how many people will participate in the auction, but you know that there is a certain distribution of people participating in your auction on the Internet.