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Classification by Decomposition: A Partitioning of the Space of 2X2 Symmetric Games
Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
2017 (Engelska)Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)Alternativ titel
Klassificering genom dekomposition : En partitionering av mängden av symmetriska 2X2 spel (Svenska)
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.

Ort, förlag, år, upplaga, sidor
2017. , s. 148
Nyckelord [en]
Game theory, Classification, 2x2 Games, Symmetric Games, Decomposition, Partition, Number of Games
Nyckelord [sv]
Spelteori, Klassificering, 2x2-spel, Symmetriska spel, Dekomposition, Partitionering, Antal spel
Nationell ämneskategori
Annan matematik
Identifikatorer
URN: urn:nbn:se:liu:diva-137991ISRN: LiTH-MAT-EX--2017/10--SEOAI: oai:DiVA.org:liu-137991DiVA, id: diva2:1106499
Ämne / kurs
Matematik
Presentation
2017-05-15, S11, Linköping, 10:06 (Svenska)
Handledare
Examinatorer
Tillgänglig från: 2017-06-09 Skapad: 2017-06-07 Senast uppdaterad: 2017-06-09Bibliografiskt granskad

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