Utility representations of preferences: some results : delo diplomskega seminarja

Tominc, Julija (author), Bosi, Gianni (mentor), Košir, Tomaž (mentor)

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.

• Language: English
• Keywords: utility function, continuity, Nachbin-Uryshon approach, Debreu separability
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2018
• PID: 20.500.12556/RUL-103790
• UDC: 519.8
• COBISS.SI-ID: 18479449
• Publication date in RUL: 26.09.2018

Secondary language

• Language: Slovenian
• Title: Funkcija koristnosti in preference: nekaj rezultatov

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.

• Keywords: funkcija koristnosti, Nachbin-Uryshon, zveznost, Debreujeva ločljivost