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master's thesis
Algoritmi određivanja Nashove ravnoteže u teoriji igara
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:787540
Zadro, Marina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Zadro, M. (2015). Algoritmi određivanja Nashove ravnoteže u teoriji igara (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:787540

Zadro, Marina. "Algoritmi određivanja Nashove ravnoteže u teoriji igara." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:787540

Zadro, Marina. "Algoritmi određivanja Nashove ravnoteže u teoriji igara." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:787540

Zadro, M. (2015). 'Algoritmi određivanja Nashove ravnoteže u teoriji igara', Master's thesis, University of Zagreb, Faculty of Science, accessed 18 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:787540

Zadro M. Algoritmi određivanja Nashove ravnoteže u teoriji igara [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2025 January 18] Available at: https://urn.nsk.hr/urn:nbn:hr:217:787540

M. Zadro, "Algoritmi određivanja Nashove ravnoteže u teoriji igara", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:787540

Metadata
TitleAlgoritmi određivanja Nashove ravnoteže u teoriji igara
AuthorMarina Zadro
MentorLavoslav Čaklović (mentor)
Committee memberLavoslav Čaklović (predsjednik povjerenstva)
Committee memberBojan Basrak (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberAnte Mimica (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U radu je objašnjeno kako pronaći Nashovu ravnotežu i subgame-perfect ravnotežu u igrama s dva igrača. Opisan je zapis igara u normalnoj i proširenoj formi te pronalazak dominantnih strategija u svakoj od formi. U četvrtom poglavlju su objašnjeni neki algoritmi pomoću kojih pronalazimo Nashovu ravnotežu u igrama s dva igrača. Pomoću tih algoritama računalo donosi odluku koju strategiju će odabrati. Poseban fokus smo stavili na algoritam \(\alpha-\beta\) podrezivanje. Taj algoritam je korišten za razvoj softvera u igri križić-kružić koji je priložen uz rad. Radi ograničenih računalnih resursa, efikasnost računala u pronalasku svoje najbolje strategije u nekoj igri ovisi o veličini stabla pretraživanja. Stablo pretraživanja je veće ukoliko je broj mogućih poteza u igri veći. Na primjer, igra križić kružić ima manji broj poteza od igre šah, pa je njeno stablo pretraživanja mnogo manje nego stablo pretraživanja u šahu. Što je stablo pretraživanja manje to će računalo točnije odrediti svoju najbolju strategiju i samim tim čovjeku će biti teže pobijediti računalo u nekoj igri.
Abstract (english)
In this thesis, the finding of Nash equilibrium and subgame-perfect equilibrium was explained for two-player games. We considered normal-form and extended-form game representation (and their respective dominant strategies). Algorithms for finding Nash equilibrium in two-player games, as explained in the fourth chapter, are the base for optimal computer strategy decision making. The focus of this dissertation is the \(\alpha-\beta\) pruning algorithm used for the making of the tic-tac-toe game attached to the thesis. The efficiency of finding optimal game strategy is greatly affected by limited computer resources. Therefore it is also closely affiliated with the size of the game search tree. The greater the game search tree, so grows the number of possible outcomes. Therefore, the smaller the search tree, the computer accuracy of finding the optimal strategy grows, and so does the difficulty of defeating the computer.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:787540
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-20 11:51:29