# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Xavier Jarque i Ribera i F. Javier  Martínez de Albéniz

# metadata.dc.description.abstract[].value
[en] Auctions are a tool used from ancient times to sell objects. They are useful, since the objects are sold competitively, especially when the actual value is unknown by the seller. W. S. Vickrey and J. Mirrlees were awarded the Nobel Prize in Economics in 1996 for their studies of the economic theory of incentives in conditions of asymmetric information. On the other hand, auctions are found in the field of the mechanisms. L. Hurwicz, E. Maskin and R. Myerson received the Nobel Prize in Economics in 2007 for describing the foundations of mechanism design theory. In this project, we study the theory of auctions of a single object with private valuations, both at first price and at second price. As a main result, we find the revenue equivalence principle concerning certain types of auction. After that we extend the study to auctions with a reservation price.
Finally, the theory of mechanism design is developed. We analyze what is a mechanism from a general point of view and then we study the auctions seen as mechanisms. The revelation principle allows to express an indirect mechanism as a direct mechanism. There are several properties worthy of being mentioned as compatibility with incentives or individual rationality. To finish this paper we describe an example of bilateral trade.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Berta Serra Aguilera, 2019

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques