Slučajne matrične igre : delo diplomskega seminarja

Bertok, Tina (author), Bernik, Janez (mentor), Šega, Gregor (co-mentor)

Slučajne matrične igre so običajne matrične igre, katerih plačila so slučajne spremenljivke. Celotna diplomska naloga temelji na primerjavi vrednosti povprečne igre ter povprečne vrednosti igre. Matrično igro predstavlja slučajna matrika. V ospredju je preizkus hipoteze, da velja različica Jensenove neenakosti in sicer da je povprečna vrednost igre vedno večja ali enaka vrednosti povprečne igre. Hipotezo smo preverili najprej na 2x2 matrikah, kasneje tudi na 3x3 matrikah.

• Language: Slovenian
• Keywords: slučajne matrične igre, vrednost igre, sedlo, Nashevo ravnovesje, teorija iger
• Work type: Bachelor thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-118035
• UDC: 519.8
• COBISS.SI-ID: 33321219
• Publication date in RUL: 15.08.2020

Secondary language

• Language: English
• Title: Random matrix games

Abstract

Random matrix games are ordinary matrix games whose payouts are random variables. The thesis is based on a comparison of the value of the average game and the average value of the game. A matrix game is a random matrix. At the forefront is a test of the hypothesis that a version of Jensen's inequality holds, namely that the average value of the game is always greater than or equal to the value of the average game. We tested the hypothesis first on 2x2 matrices, later also on 3x3 matrices.

• Keywords: random matrix games, game value, saddle point, Nash equilibrium, game theory