Utility representations of preferences: some results

delo diplomskega seminarja

Julija Tominc (Author), Gianni Bosi (Mentor), Tomaž Košir (Mentor)

Abstract

The thesis presents some classical results concerning the Utility Theory. We present the requirements that a preorder must satisfy in order to be representable with a utility function while also exploring weaker conditions such as in the case of quasi-preorders. We establish the existence of a utility function, and explore the requirements for its upper semi-continuity in the form of the Rader theorem. Further using the Uryshon-Nachbin approach we present the proofs for both the classical Debreu theorem and the Eilenberg theorem, guaranteeing us the existence of a continuous utility on second countable topological spaces and connected separable topological spaces, respectively.

Keywords

mathematics;utility function;continuity;Nachbin-Uryshon approach;Debreu separability;

Data

Language:	English
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[J. Tominc]
UDC:	519.8
COBISS:	18479449
Views:	616
Downloads:	235
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Funkcija koristnosti in preference: nekaj rezultatov
Secondary abstract:	Delo diplomskega seminarja predstavi nekaj klasičnih rezultatov teorije koristnosti začenši z zahtevami za obstoj funkcije koristnost za totalne binarne relacije. Dodatno predstavimo šibkejše zahteve, ki zadostujejo za obstoj funkcije koristnosti za binarne relacije, ki niso tranzitivne. Nadaljujemo z raziskovanjem zahtev za zveznost funkcije koristnosti na 2-števnem topološkem prostoru v obliki Debreujevega izreka in obstoja zvezne funkcije na povezanem in separabilnem topološkem prostoru, ki je predstavljen z Eilenbergovim izrekom. Izreka dokažemo s pomočjo Nachbinove razširitve Uryshonovega dela.
Secondary keywords:	matematika;funkcija koristnosti;Nachbin-Uryshon;zveznost;Debreujeva ločljivost;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja, Program dvojne diplome iz matematike z Univerzo v Trstu
Pages:	28 str.
ID:	10961999