Show simple item record

dc.contributor.authorHEDGES, JMen_US
dc.contributor.editorOliva, Pen_US
dc.contributor.editorRobinson, Een_US
dc.descriptionI gratefully acknowledge that my PhD studies were funded by EPSRC doctoral training grant EP/K50290X/1.en_US
dc.descriptionI gratefully acknowledge that my PhD studies were funded by EPSRC doctoral training grant EP/K50290X/1.en_US
dc.description.abstractWe introduce a new foundation for game theory based on so-called open games. Unlike existing approaches open games are fully compositional: games are built using algebraic operations from standard components, such as players and outcome functions, with no fundamental distinction being made between the parts and the whole. Open games are intended to be applied at large scales where classical game theory becomes impractical to use, and this thesis therefore covers part of the theoretical foundation of a powerful new tool for economics and other subjects using game theory. Formally we defi ne a symmetric monoidal category whose morphisms are open games, which can therefore be combined either sequentially using categorical composition, or simultaneously using the monoidal product. Using this structure we can also graphically represent open games using string diagrams. We prove that the new de finitions give the same results (both equilibria and o -equilibrium best responses) as classical game theory in several important special cases: normal form games with pure and mixed strategy Nash equilibria, and perfect information games with subgame perfect equilibria. This thesis also includes work on higher order game theory, a related but simpler approach to game theory that uses higher order functions to model players. This has been extensively developed by Martin Escard o and Paulo Oliva for games of perfect information, and we extend it to normal form games. We show that this approach can be used to elegantly model coordination and di fferentiation goals of players. We also argue that a modifi cation of the solution concept used by Escard o and Oliva is more appropriate for such applications.en_US
dc.description.sponsorshipEPSRC doctoral training grant EP/K50290X/1.en_US
dc.rightsThe copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author
dc.subjectGame theoryen_US
dc.subjectOpen gamesen_US
dc.titleTowards compositional game theoryen_US
pubs.notesNo embargoen_US

Files in this item


This item appears in the following Collection(s)

  • Theses [2961]
    Theses Awarded by Queen Mary University of London

Show simple item record