Multi-unit Auction Theory And The Analysis Of Its Models

The auction has a long history of trading in the market. It is approved by the buyers and sellers in the market and the general public because of its uniquely open, fair and righteous characteristics. Vickrey, who won the Nobel Prize in Economics, made a great contribution to the auction theory. Based on the assumptions of private value, type of independent, symmetry and the risk neutral, he proved that the four standard auctions had the same revenues. Although this conclusion relied on the strict assumptions, it stilly could simplify many economic and social problems. With the development of economy, more and more multi-unit auctions are researched in practice. Therefore, the multi-unit auction theory draws more and more attentions to the economists and is becoming the most active research field in the auction theory. The research on multi-unit auction not only can promote the development of economic theory, but also has a very important significance on the reform development of the China's economic system.This paper studies the multi-unit auction mechanism to maximize the seller's expected utility of the goods based on a relatively simple model. Firstly, I introduce the research aim and signification of this paper, and review the birth and development of auction. Secondly, the basic auction theories and the basic models are given. Thirdly, I give a number of assumptions about the model. I also design the optimal auction mechanisms according to the assumptions. Then, I study the mechanisms for the implementation of the optimal auction in the unit-demand symmetrical model. Finally, I present the symmetrical private signal model with two bidders and two goods, and use a simple geometric relationship to explain the optimal auction.