diplomsko delo
Andreja Smole (Avtor), Drago Bokal (Mentor)

Povzetek

V diplomskem delu smo analizirali problem ocenjevanja med profesorjem in študentom z uporabo teorije iger. S pomočjo Nashevega ravnovesja igre smo raziskovali optimalne pogoje in motivacijo v šolskem sistemu, ki bi tako profesorje kot študente spodbudili k čim boljšemu delu in na ta način prispevali k boljšemu izobraževanju. V prvem delu smo spoznali teorijo iger. Skozi kratek zgodovinski pregled smo spoznali nastanke teorije iger in pomembne izsledke matematikov, ki so delovali na tem področju. V nadaljevanju smo opredelili osnovne pojme teorije iger ter definicijo igre in igralca. Prav tako smo okarakterizirali posamezne tipe iger, njihove lastnosti, način igranja in poiskali Nasheva ravnovesja iger za vsak tip igre. Drugi del diplomskega dela preučuje igro ocenjevanja med profesorji in študenti. V opisu igre smo spoznali kontekst igre, število ocen, trajanje igre, tip igre, tabelo igre, diagram poteka igre, opis igralcev in njihova plačila in si ogledali posamezne dvoboje in plačila, ki nastopijo ob igri različnih strategij. Uvedli smo tri komponente plačilne funkcije: znanje, prosti čas in oceno. Poiskali smo optimalne okoliščine v šolstvu, ki bi motivirala študente in profesorje k čim boljšemu delu in na ta način predlagali izboljšave, ki vodijo do boljšega znanja študentov. Z analizo igre v različnih okoliščinah, ki nastanejo ob različni obtežitvi komponent plačil, smo ugotovili, da lahko izberemo tak sistem nagrajevanja, v katerem nastopi Nashevo ravnovesje natanko takrat, ko profesor izbere strategijo 'vloži veliko truda in realno oceni' in študent izbere strategijo 'vloži veliko truda in realno oceni' ali strategijo 'vloži veliko truda in nerealno oceni'.

Ključne besede

matematika;teorija iger;odločitve;igre;popolna informacija;nepopolna informacija;Nashevo ravnovesje;profesorji;študenti;diplomska dela;

Podatki

Jezik: Slovenski jezik
Leto izida:
Izvor: Maribor
Tipologija: 2.11 - Diplomsko delo
Organizacija: UM FNM - Fakulteta za naravoslovje in matematiko
Založnik: [A. Smole]
UDK: 51(043.2)
COBISS: 18616840 Povezava se bo odprla v novem oknu
Št. ogledov: 1892
Št. prenosov: 388
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Ostali podatki

Sekundarni jezik: Angleški jezik
Sekundarni naslov: MORAL HAZARD IN EDUCATION: ANALYSIS OF NASH EQUILIBRIA ON PROFESSOR - STUDENT GAMES
Sekundarni povzetek: In the diploma thesis we analyzed the problem of grading between professors and students with the use of game theory. With the help of the Nash equilibrium we determined optimal conditions and motivation in school system which would stimulate both the students and professors to do their best and as such would contribute to better education. In the first part of the diploma thesis, we introduced the game theory. Through a brief history review we get to know how the game theory has developed and some important results of mathematicians that were active in this field. Further we defined the basic concepts of the game theory and definition of the game and its player. We characterized individual game types, their characteristics, the way of play and defined the Nash equilibrium for each type of the game. The second part studies the grading game between professors and students. In the description of the game we get to know the game contexts, number of grades, game duration, game type, game table, diagram of the game course, description of the players and their payouts. We also examined individual duels and their payouts that are the results of different game strategies. We introduced three components of the utility function: knowledge, spare time, grade and then looked for the optimum situation in educational system that would motivate students and professors to do their best. By doing this we then suggested improvements in the system that would lead to better student knowledge. With game analysis in different situations which are the result of different weights of the components we established that in the game with four-level knowledge reward system respecting certain rational assumptions on relative weights of utility function components, it is possible to design utility functions, such that Nash equilibrium of the game is for the professor to choose the strategy of quality work and realistic grading and for the student to choose the strategy of quality work and realistic grading or the strategy of quality work and nonrealistic grading.
Sekundarne ključne besede: game theory;decision;games;games with perfect information;games with imperfect information;Nash equilibrium;professor-student games;
URN: URN:SI:UM:
Vrsta dela (COBISS): Diplomsko delo
Komentar na gradivo: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Strani: 186 f.
Ključne besede (UDK): mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID: 19495