Mechanism Design For Combinatorial Auctions And Study On Cooperative Problems In Auctions

Auctions, as one of transaction means, have been used in the transaction of all kinds of commodities in the past thousands of years. Tody, people have been accustomed to accept auctions as a common mechanism to sell some resources Many commodities are sold by auctions, including perishable goods such as cat-tles、fishes and flowers, cattles、fishes and flowers such as work of art、houses and wine, abstract goods such as state treasury bond、UMTS license, even beauty contest had ever introduced auction method.FCC auction in America made a great success and caught many economists’ eyes, as a consequence, sequential auctions also have attracted much attention. Since a rational seller would choose a transaction mechanism that maximize his ex ante expected revenue, mechanism design problem occurs. Even though easy op-erational much-loved sequential auctions are chosen, the seller can also improve his expected revenue by some methods. We introduce quantity discount and explore mechanism design problem to determine the optimal discount amount. Mechanism design problems are set up on the base of incentive compatibility and individual rationality, incentive compatibility denotes that it’s the optimal choose for each buyer to bid according to his own true type, which involves in another important problem of auction theory—the buyers’ equilibrium bidding strate-gies. In an auction, a buyer’s equilibrium bidding strategy is impacted by many factors—auction formats、distributions of the buyers’ types、utility functions, we consider some uncertain factors and payment of the price. Meanwhile, as a successful application of game theory, auction theory naturally involves in coop-erative game when cooperative game and non-coopeartive game intersect, how to divide cooperation interests when grand coalition among all the buyers forms and how believable threat influences the benefit distribution belong to the problems we would study.Against two kinds of auction problems, this thesis studies the buyers’ equi-librium bidding strategies and uncertain factors impact on them in single object auction、the mechanism design problem of choosing the optimal quantity dis-count amount and general mechanism design problems、cooperation in auction and cooperative profit distribution problems.Firstly, we derive the essential condition a buyer’s equilibrium bidding strat-egy satisfies in asymmetric first price auction when all the buyers are risk-averse and have the same utility function, then study the reverse hazard rate’s im-pact on the buyers’bids. We give the approximate computational formulas of the buyers’equilibrium bidding strategies and the seller’s expected revenue by perturbation method when all the buyers are symmetric and weakly risk-averse. We also study auctions that payment based on the first price auction and sec-ond price auction、all-pay auction and war of attrition when the buyers have correlated types and common value, derive the buyers’symmetric equilibrium bidding strategy and work out the seller’s expected revenue, analyze variation of the weighting factors’s impact on the buyers’bidding strategy and the seller’s expected revenue.Secondly, we introduced quantity discount into sequential auctions that are used in common auction activities, study how to chose the optimal discount amount for the seller to maximize his ex ante expected revenue. Objects in the discussed problems can be homogeneous substitutes or stochastic equivalent com-plements、discount way can be fixed scalar or fixed proportion, so there are four kinds of problems. We analyze quantity discount’s impact on the buyers’bid and the seller’s expected revenue. When adopting fixed scalar discount, we study the buyers’number、synergy factor and the buyers’strength’s impact on the optimal discount amount and the seller’s expected revenue for the sale of homo-geneous substitutes, we also study the relationship between the optimal discount amount and the buyers’number, the seller’s expected revenue and complemen-tarity among objects for the sale of stochastic equivalent complements. When adopting fixed proportional discount, analytical results of optimal discount for corresponding problem are derived.Thirdly, we study multiple auction mechanism design problem of private value model and interdependent value model with multiple objects and buyers who have multiple demand and independent types, extend the revenue equivalence theorem from private value model to interdependent value model. We also derive the buyers’expected utility when they bid according to his true types for when there are two objects and the buyers have multiple demand, from which we work out the seller’s ex ante expected revenue and determine the optimal allocation rule and payment rule. Under VCG mechanism in which the buyers undertake the transaction fee, we discuss transaction fee’s impact on the buyers’、the buyer’s and the social surplus, consider some special cases including bundle sales、some buyer wins all the objects and only two objects for sale. In the end, we translate a general VCG mechanism into a0-1integer programming problem.Lastly, we analyze the essence of cooperative game, indicate that the cause cooperation forms includes not only the common two basic conditions—oop-erative improve both group and individual’s revenue, but cognitive consistency among the players plays an important part. Giving several concepts about co-operative game and cooperative solution, we discuss benefit distribution problem in the second price auction when grand coalition forms among all the buyers. We define the cooperative game, discuss its core, figure out its Shapley value and Banzhaf value and analyze their peculiar properties, give Nash bargaining solution based on bargaining ability. For the cooperative problem with believable threat, we give cooperative solution when all the buyers stick to some strategy.