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Classification by Decomposition: A Partitioning of the Space of 2X2 Symmetric Games
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
2017 (English)Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesisAlternative title
Klassificering genom dekomposition : En partitionering av mängden av symmetriska 2X2 spel (Swedish)
Abstract [en]

Game theory is the study of strategic interaction between rational agents. The need for understanding interaction arises in many different fields, such as: economics, psychology, philosophy, computer science and biology. The purpose of game theory is to analyse the outcomes and strategies of these interactions, in mathematical models called games. Some of these games have stood out from the rest, e.g. Prisoner's Dilemma, Chicken and Stag Hunt. These games, commonly referred to as the standard games, have attracted interest from many fields of research. In order to understand why these games are interesting and how they differ from each other and other games, many have attempted to sort games into interestingly different classes. In this thesis some already existing classifications are reviewed based on their mathematical structure and how well justified they are. Emphasis is put on mathematical simplicity because it makes the classification more generalisable to larger game spaces. From this review we conclude that none of the classifications captures both of these aspects. We therefore propose a classification of symmetric 2x2 games based on decomposition. We show that our proposed method captures everything that the previous classifications caputure. Our method arguably explains the interesting differences between the games, and we justify this claim by computer experiments. Moreover it has a simple mathematical structure. We also provide some results concerning the size of different game spaces.

Place, publisher, year, edition, pages
2017. , 148 p.
Keyword [en]
Game theory, Classification, 2x2 Games, Symmetric Games, Decomposition, Partition, Number of Games
Keyword [sv]
Spelteori, Klassificering, 2x2-spel, Symmetriska spel, Dekomposition, Partitionering, Antal spel
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-137991ISRN: LiTH-MAT-EX--2017/10--SEOAI: oai:DiVA.org:liu-137991DiVA: diva2:1106499
Subject / course
Mathematics
Presentation
2017-05-15, S11, Linköping, 10:06 (Swedish)
Supervisors
Examiners
Available from: 2017-06-09 Created: 2017-06-07 Last updated: 2017-06-09Bibliographically approved

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Böörs, MikaelWängberg, Tobias
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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf