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

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

John Adams Smith letter, Jan. 14, 1813

Transcript: New York Jan. 14. 1813. My dear uncle, I had nearly concluded to have made my [jaunt?] earlier than I had mentioned in my last letter to you, for Swartout had intended to have written by me to Father & yourself; having [Louisa?] concluded not so soon to depart he sends me his letters which I forward in mail, I shall hope to have letters from home soon, it is a great pleasure to hear from any of you. I said last week in Hollands letter mentioning [bladeworth?] account, I have explained to him. It is a mistake about me agreeing to pay Mr. [Dening?] [their?] account. Caroline mentions to me your jaunt to [Sophia?], but I regret our friend there should be unpleasantly situated. I have not yet seen Col. Willett but will see him as mentioned. I have neglected to go there for some time which has been remiss in me. We have nothing new I believe unless it be that Armstrong & Jones of Philadelphia have been nominated as Secretarys of War & the Navy & [cer?] this in all probability may be appointed. There may be room for speculation, but perhaps it is not probable that Canada will be ceded to American Valor in the year 1813. There is a Bill before congress by which it may be made penal to enter on board American vessels, either British subjects or naturalized Americans, which it is presoomed by many will [spon?] the accommodation of Peace – may be yes may be no – the proof of the pudding is in the eating of it. I imagine pacification is not so near at hand although it is much to be desired. Whatever might be for the honor & prosperity of the Country I would strenuously advocate, aloof from partial & party considerations. We have not a word as yet what the Council at Albany may be thinking of as yet. I suppose these things will come in time, perhaps untimely to many. I desire for the present not to be found among the untimely. I am your sincerely, with love to all. John Adams Smith

Letter - Bliss Carman to Ethelwyn Wetherald, 15 Decemer 1897

This letter from William Bliss Carman to Ethelwyn Wetherald in 1897, includes a photo of Carman with Miss M. B. Stevenson from the year 1927. Carman, originally from Canada, had great success as