The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

摘要

This work consists of a theoretical part and an experimental one. The first partprovides a simple treatment of the celebrated von Neumann minimax theorem asformulated by Nikaid6 and Sion. It also discusses its relationships with fundamentaltheorems of convex analysis.The second part is about externality in sponsored search auctions. It shows that inthese auctions, advertisers have externality effects on each other which influence theirbidding behavior. It proposes Hal R.Varian model and shows how adding externalityto this model will affect its properties. In order to have a better understanding ofthe interaction among advertisers in on-line auctions, it studies the structure of theGoogle advertisements networ.k and shows that it is a small-world scale-free network.