Introdução à teoria matemática dos leilões - Igor Soares dos Santos Barbosa (2023)
This dissertation is about unique item auctions, the mathematical model used supposes all participants have linear utility and rationality, the set of strategies is always a Nash equilibrium, and the probability distributions of the private values are known for all participants. We present classical results and classic auction mechanisms, such as the Revenue Equivalence Theorem of Vikrey and of Myerson, the revelation principle, English auction, Dutch auction, and Vickrey's auction. Some other fresh results as an approximately optimal auction of Lookahead (by Ronen) are present in Chapter 4. When the values are independent and absolutely continuous Myerson showed that an optimal auction can be found, this is done in Chapter 3, in the last chapter presents how to reduce the problem of finding an optimal auction to a problem of linear programming in the case of discrete values.