MATH EXPLORERS' CLUB Cornell Department of Mathematics 


Throughout these lessons we present a brief introduction to the main concepts and results of Auction Theory, an applied branch of Game Theory that has a theoretical structure worthy of explanation.

The first item bought on e-bay was a broken laser pointer for $14.83. When asked if he understood the laser pointer was broken, the buyer answered: "I'm a collector of broken laser pointers."
The material is divided in four lessons. In lesson 1 we explain why auctions are worthy of study and list the main assumptions we will make in the subsequent lessons from a game-theoretical point of view. There exist four main kinds of auctions: the English auction, the Dutch auction, the first-price sealed-bid auction and the second-price sealed-bid or Vickrey's auction (essentially equivalent to e-bay's auction style, see figure). In lesson 2 we will describe the English auction (the most common type of auction) and the second-price sealed-bid or Vickrey's auction establishing the relationship between the two. In lesson 3 we will describe and establish the relationship between the Dutch and first-price sealed-bid auctions. Finally, lesson 4 will be devoted to the statement of the celebrated Revenue Equivalence Theorem and the exposition of some more general models in which the assumptions listed in lesson 1 do not necessarily hold.
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