| This thesis mainly study multi-unit auctions in social networks,where each buyer has a budget limit(public or private)and can spread the sale information to the network neighbors.In the model of this thesis,there is only one seller with m items(divisible or indivisible).This thesis focuses on analyzing the social welfare or the seller revenue of the mechanism.In general,social welfare maximization and seller revenue maximization are two conflicting but important design criteria in auction design.The social welfare maximization mechanism allocates the items to the buyer with the highest bid.Differently,the seller revenue maximization mechanism wants to maximize the seller's revenue.This thesis has two main contributions:(1)For the social network public budget auction model,new set expansion rules and price increase rules are designed to extend the classical clinching mechanism to social network auction scenarios.This thesis detailedly describes the price characteristics of the clinching mechanism and gives a polynomial algorithm which can compute the critical price.This thesis proves some important properties of social network clinching mechanism,such as no positive transfer,individual rationality,incentive compatibility,non-wasteful and social welfare guarantee.(2)For the social network private budget auction model,due to the distributional complexity of social networks,it is difficult to estimate the prior distribution that Myerson-type auctions needs.This thesis designs a seller revenue maximization mechanism that does not depend on prior distribution by random sampling technology.By the concept of random spanning tree and sampling subtree,the difficulty of obtaining prior distribution in the complex social network environment is solved.This thesis proves the truthful,individual rationality,budget feasibility and computational efficiency of the revenue maximization mechanism.This thesis is the first work to extend social network auctions to more general auction scenarios. |
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