Fixed point, game and selection theory: from the hairy ball theorem to a non hair-pulling conversation

DSpace/Manakin Repository

Show simple item record

dc.contributor.advisor Gourdel, Pascal it_IT Maagli, Nadia <1987> it_IT 2016-06-27 it_IT 2016-12-15T08:16:01Z 2016-12-15T08:16:01Z 2016-07-02 it_IT
dc.description.abstract This PHD dissertation develops fixed point theory issues. Fixed point theory is at the heart of the nonlinear analysis. One amongst the first and famous results is Brouwer's fixed point theorem (1910). Two years after, Brouwer proved another topological result. The first chapter of this thesis is dedicated to this result. Namely, the hairy ball theorem. We introduced an equivalent version of the hairy ball theorem in the form of a `fixed point theorem'. In this way, ensuring the proof of this equivalent theorem gives a new insight on the hairy ball theorem. On the other hand, the theorem of Brouwer was extended in many ways. The first extension was made by kakutani who generalised the result for multifunctions. More precisely, he ensured the exsitence of fixed point theorem for upper semicontinuous correspondence. Yet, since the upper semicontinuity and the lower semincontinuity are two notions generalizing the classical continuity for single valued functions, then one can ask the following question: What about the class of lower semicontinuous correspondences? This class plays a major role in selection theory and chapter 2 of this thesis is related to Michael's selection theorem. We proved a selection theorem related to one result of Michael. One of the most important tools in order to prove our result is the introduction of a new concept of convex analysis: The peeling concept. Finally, it is known that Kakutani's fixed point theorem has many applications. Namely, in game theory. Indeed, it has a vital connection with the Nash equilibrium theorem. The last chapter of this thesis presents an unusual application of Brouwer's fixed point theorem and the Nash equilibrium theorem in order to modelise a non-cooperative game. We have two agents, endowed with their own individual convex categorisations, negotiate over the construction of a common convex categorisation. The common convex categorisation emerges as the (unique) equilibrium of the game it_IT
dc.language.iso en it_IT
dc.publisher Università Ca' Foscari Venezia it_IT
dc.rights © Nadia Maagli, 2016 it_IT
dc.title Fixed point, game and selection theory: from the hairy ball theorem to a non hair-pulling conversation it_IT
dc.title.alternative it_IT
dc.type Doctoral Thesis it_IT Economia it_IT Dottorato di ricerca it_IT Dipartimento di Economia it_IT
dc.description.academicyear 2014/2015, proroghe semestrali 2014/2015 it_IT
dc.description.cycle 27 it_IT Pasini, Giacomo <1976> it_IT
dc.location.shelfmark D001638 it_IT
dc.location Venezia, Archivio Università Ca' Foscari, Tesi Dottorato it_IT
dc.rights.accessrights openAccess it_IT
dc.thesis.matricno 956046 it_IT
dc.format.pagenumber XII, 92 p. it_IT
dc.description.note it_IT it_IT Li Calzi, Marco it_IT
dc.provenance.upload Nadia Maagli (, 2016-06-27 it_IT
dc.provenance.plagiarycheck Marco Li Calzi (, 2016-07-01 it_IT

Files in this item

This item appears in the following Collection(s)

Show simple item record