# Algoritmi određivanja Nashove ravnoteže u teoriji igara

Zadro, Marina (2015) Algoritmi određivanja Nashove ravnoteže u teoriji igara. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: Croatian

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.