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master's thesis
Polinomski sustavi u ekonomiji
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:558037
Zemunik, Petra
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Zemunik, P. (2018). Polinomski sustavi u ekonomiji (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:558037

Zemunik, Petra. "Polinomski sustavi u ekonomiji." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:558037

Zemunik, Petra. "Polinomski sustavi u ekonomiji." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:558037

Zemunik, P. (2018). 'Polinomski sustavi u ekonomiji', Master's thesis, University of Zagreb, Faculty of Science, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:558037

Zemunik P. Polinomski sustavi u ekonomiji [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:217:558037

P. Zemunik, "Polinomski sustavi u ekonomiji", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:558037

Metadata
TitlePolinomski sustavi u ekonomiji
AuthorPetra Zemunik
MentorDragutin Svrtan (mentor)
Committee memberDragutin Svrtan (predsjednik povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-03-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Glavni cilj ovog rada je proučiti pojam Nashove ravnoteže te pokazati rezultate koji daju maksimalan broj mješovitih Nashovih ravnoteža u igri s \(n\) igrača. Nashove ravnoteže karakteriziramo kao rješenja određenih polinomskih sustava. Sustav polinoma možemo riješiti metodom Gröbnerovih baza pa se u prvom poglavlju upoznajemo s njihovom definicijom i svojstvima. Broj rješenja polinomskog sustava možemo izračunati uz pomoć mješovitog volumena Newtonovih politopa. U drugom poglavlju prvo se prisjećamo konveksnosti, a zatim upoznajemo sa sumom Minkowskog i mješovitim volumenom politopa. Treće poglavlje konačno definira Nashovu ravnotežu te daje rezultate o broju mješovitih Nashovih ravnoteža koji proizlaze iz Bernstein-Kushnirenkovog teorema.
Abstract (english)
The main goal in this master thesis is to study the concept of Nash equilibrium and to show results that give a sharp bound for the number of totally mixed Nash equilibria in a \(n\)-person game. Nash equilibria are characterized as the solutions of certain polynomial systems. The polynomial system can be solved by the method of Gröbner bases, so in the first chapter we introduce their definition and properties. The number of solutions of a polynomial system can be found by computing the mixed volume of Newton polytopes. In the second chapter, we recall the convexity, Minkowski sum and mixed volume of several polytopes. In the third chapter, Nash equilibrium is finally defined and results on the number of totally mixed Nash equilibria are given by using Bernstein-Kushnirenko theorem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:558037
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-11-21 09:29:27