Research On Auction Design By Numerical Simulation

Auction is a transaction way that has a very long history, and be the most institution used in the property transaction in the overseas. Now property transaction in China is becoming more and more, and the related value is increasing firmly. The transacted properties include forestry resource, ore-mining right, land-developing right, spectrum license and pollutants discharging rights. The survey shows that the transactions of these nation-owned properties are mainly in the form of negotiation. So these transactions have strong color of planned economy. The government often give direction to the them at will, not on the base of scientific analysis. Many negative effects are caused by this kind of transactions. For example, there is often some entanglements on the property left after the transaction was done, because of the unreasonable pricing under the government direction. Therefore, the auction must be proposed to the transaction of the nation-owned property in the future, and the construct the normal transaction institution should be constructed to eliminate the social contradiction and promoted the harmony in the society. Thus, the research on the auction should be strengthened. The Chinese enterprises has begun the internationalized running. They have paid costly expense for the purchasing the overseas property, such as Ping An Insurance (Group) Company Of China purchasing the equity of Fortis Haitong Annuities, or Chinalco purchasing the equity of Rio Tinto. Thus, better understanding of the auction behavior can offer better reference for the overseas acquisition to avoid paying high price.In this paper, the following topics are include.①The risk-neutral seller's auction design under the condition of symmetric private value. On the base of the past theories derived from the analytic model, this paper makes the numerical simulation of auction by Monte Carlo method, and draws the diagram of the seller's'Expected Income - Reserve Price'curve. Four kinds of valuation information are included, that is, left-hump, central hump, right-hump and uniform distribution. At the same time, two different buyer's quantity are considered, that is, 5 buyers and 10 buyers. These curves show that the seller's expected income is not sensitive to the reserve price. This result can simplify the auction design largely.②The risk-averse seller's auction design under the condition of symmetric private value. On the base of the conclusion about the risk-neutral seller, employ Monte Carlo method to draw the diagram of"Standard Deviation of Income– Reserve Price"curve. The diagram also include the cases corresponding to those four distributions and two buyer's quantities. This paper use the data generated by Monte Carlo simulation to show the distribution of the seller's income.③The buyer's equilibrium bidding strategy. The'Revenue Equivalence Principle'fails for the buyers are not symmetric. So the buyers'equilibrium bidding strategies are necessary for the calculation of the seller's income. This paper considers two kinds of auction rule, that is, the second-price sealed-bid auction and the first-price sealed-bid auction. The buyer's equilibrium bidding strategy in the second-price sealed-bid auction is very simple, bidding price equal to the value of the item. But things are much more complicated for the first-price sealed-bid auction. In this paper, the first-order condition of the equilibrium is found by variation method, and it tells that the buyer's equilibrium bidding strategy can not be got in the analytic form. So the equilibrium bidding strategy must be calculated in the numerical form from the first-order condition.④The auction design under the condition of asymmetric private value. For the'Revenue Equivalence Principle'fails under the condition of asymmetric buyers, different auction rules will produce different expected income for the seller. Then the so-called auction is design is to select a optimal auction rule from several given ones, and the selection is according to the comparison of the seller's expected income calculated in the concrete environments. In this paper, the seller's'Expected Income– Reserve Price'curves of the two auction rules are calculated by the buyers'equilibrium bidding strategies. According these curves, the seller can determine which rule is better, and how to set the reserve price. The conclusion is that the setting reserve price under the condition of asymmetric buyers is like the one under the condition of symmetric buyers.⑤The collusion behavior of the buyers. This paper considers the simplest collusion, the collusion in the auction with symmetric buyers. Even in this simple case, the collusion behavior will cause the asymmetric condition. So the analysis on the asymmetric auction design relies the results about the buyer's equilibrium strategy in the asymmetric environments. In this paper, the collusion behavior in the second-price sealed-bid auction and the first-price sealed-bid auction are considered. The seller's'Expected Income– Reserve Price'curve are calculated under different auction rule and with different coalition dimensions. The conclusion is that the first-price sealed-bid auction can defend collusion better than the second-price sealed-bid auction. The curves also show that the loss of the seller's income increases monotonically as the coalition dimensions in the second-price sealed-bid auction, but not in the first-price sealed-bid auction. The collusion behavior of the buyers could sometimes increase the seller's expected income.Generally, the numerical simulation method used in this paper can solve the auction design in the concrete environments with private value. The shortcoming of this paper is that the common value auction had not be included.