OPTIMAL RESERVE PRICE IN STATIC AND DYNAMIC SPONSORED SEARCH AUCTIONS

Sponsored search advertising is a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers＇ bidding. This paper studies the optimal reserve price for a generalized second-price auction （GSP） under both static and dynamic settings. We show that if advertisers＇ per-click value has an increasing generalized failure rate, the search engine＇s revenue rate is quasi-concave and hence there exists an optimal reserve price under both settings. Different from a static GSP auction where the optimal reserve price is proved to be constant, in a dynamic setting the optimal reserve price is dependent on not only advertisers＇ per-click values, but also the number of ad links sold. A search engine should gradually raise reserve price as more qualified advertisers arrive, and maintain the same threshold after all first-page positions are occupied.

Hidden Reserve Prices with Risk-Averse Bidders

In this paper, we provide an alternative explanation for why auctioneers often keep the reserve price hidden or secret. We consider a standard independent private values environment in which the buyers are risk-averse and the seller has private information about her valuation of the object to be auctioned. The seller uses a first-price sealed-bid auction mechanism combined with either an announced reserve price or a hidden reserve price. We compare the seller＇s ex ante expected profits under these two policies and find that the optimal hidden reserve price policy generates higher expected profits for the seller when the buyers are fairly risk-averse under particular restrictions on buyers＇ preferences and the distributions of private values. As the number of the buyers increases, the hidden reserve price is more likely to dominate. Numerical methods are used to demonstrate the generality of our main results.

China’s Price System Jeopardizes its Grain Reserves

2008 is a year of bumper harvest in summer grain across China. The failure of numerous state-owned grain depots to purchase grain in times of bumper harvest, however, directly threatens grain reserve security and state control over grain prices in the upcoming year. An important factor underpinning the difficulty of state grain depots to purchase grain is the unwillingness of farmers to sell grain due to the excess of the current market price over the government "protected price" aimed at preventing cheap grain from harming farmers. When grassroots grain depots find themselves in trouble, foreign capital stealthily moves in by taking advantage of this situation. To fulfill grain storage tasks and receive various state subsidies, some state-owned grain depots have no alternative but to surreptitiously raise the purchase price. By contrast, some not so courageous state-owned grain depots can only borrow money to finance the purchase of commodity grain at market prices and subsequently figure out a way to pay back such loans. Behind such distorted grain purchase behavior lies a rough and rugged history of grain price reform in China.

Optimizing continuous cover management of boreal forest when timber prices and tree growth are stochastic

Background： Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to biased advice on optimal forest management. The study optimized continuous cover management of boreal forest in a situation where tree growth, regeneration, and timber prices include uncertainty. Methods： Both anticipatory and adaptive optimization approaches were used. The adaptive approach optimized the reservation price function instead of fixed cutting years. The future prices of different timber assortments were described by cross-correlated auto-regressive models. The high variation around ingrowth model was simulated using a model that describes the cross- and autocorrelations of the regeneration results of different species and years. Tree growth was predicted with individual tree models, the predictions of which were adjusted on the basis of a climate-induced growth trend, which was stochastic. Residuals of the deterministic diameter growth model were also simulated. They consisted of random tree factors and cross- and autocorrelated temporal terms. Results： Of the analyzed factors, timber price caused most uncertainty in the calculation of the net present value of a certain management schedule. Ingrowth and climate trend were less significant sources of risk and uncertainty than tree growth. Stochastic anticipatory optimization led to more diverse post-cutting stand structures than obtained in deterministic optimization. Cutting interval was shorter when risk and uncertainty were included in the analyses. Conclusions： Adaptive optimization and management led to 6%-14% higher net present values than obtained in management that was based on anticipatory optimization. Increasing risk aversion of the forest landowner led to earlier cuttings in a mature stand. The effect of risk attitude on optimization results was small.

OPTIMAL STARTING PRICE FOR EBAY-LIKE ONLINE AUCTIONS

Reserve price auctions are one of hot research issues in traditional auction theory. Here we study the starting price in an online auction, the counterpart of the public reserve price in a traditional auction. By considering three features of eBay-like online auctions： stochastic entry of bidders （subject to Poisson process）, insertion fee proportional to the starting price, and time discount, we have analyzed the properties of extremum points of the starting price for maximizing the seller＇s expected revenue, and found that, under certain conditions, the optimal starting price should be at the lowest Mlowable level, which is contrary to the results from the classic auction theory and finds its optimality in reality. We have also developed a general extended model of multistage auctions and carried out analysis on its properties. At last, some directions for further research are also put forward.