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Title:MORALNO TVEGANJE V IZOBRAŽEVANJU: ANALIZA NASHEVIH RAVNOVESIJ V IGRI MED PROFESORJEM IN ŠTUDENTOM
Authors:ID Smole, Andreja (Author)
ID Bokal, Drago (Mentor) More about this mentor... New window
Files:.pdf UNI_Smole_Andreja_2011.pdf (2,94 MB)
MD5: BB8B3154B4D25AA0534B566FB1D16445
PID: 20.500.12556/dkum/2e8b02b1-e769-4c42-b57d-85e49c91c6c3
 
Language:Slovenian
Work type:Undergraduate thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract: V diplomski nalogi 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 vzpodbudili 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 in definicijo igre ter igralca. Prav tako smo okarakterizirali posamezne tipe iger, njihove lastnosti, način igranja in poiskali Nasheva ravnovesja iger za vsak tip igre. Drugi del diplomske naloge 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 optimalno situacijo 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 situacijah, ki nastanejo ob različni obtežitvi komponent plačil, smo ugotovili, da lahko izberemo tak sistem nagrajevanja, v katerem nastopi Nashevo ravnovesje natanko tedaj, ko profesor izbereta strategijo 'vloži veliko truda in realno oceni' in študent izbereta strategijo 'vloži veliko truda in realno oceni' ali strategijo 'vloži veliko truda in nerealno oceni'.
Keywords:teorija iger, odločitve, igre, igre s popolno informacijo, igre z nepopolno informacijo, Nashevo ravnovesje, igre med profesorjem in študentom
Place of publishing:Maribor
Publisher:[A. Smole]
Year of publishing:2011
PID:20.500.12556/DKUM-19630 New window
UDC:51(043.2)
COBISS.SI-ID:18616840 New window
NUK URN:URN:SI:UM:DK:ZKN9FRNY
Publication date in DKUM:12.09.2011
Views:2662
Downloads:459
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:MORAL HAZARD IN EDUCATION: ANALYSIS OF NASH EQUILIBRIA ON PROFESSOR - STUDENT GAMES
Abstract: 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.
Keywords:game theory, decision, games, games with perfect information, games with imperfect information, Nash equilibrium, professor-student games


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