Simplification, Classification, and Network Behaviors in Game Theory
Claes, Nathan Joseph
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The present research will explore potential new developments in an analytic approach to the study of interaction, game theory. The first chapter provides an overview and introduction to the mechanisms used by the social sciences to model and understand the principles of human interaction. That overview in turn gives rise to a discussion of the specific elements of game theory, and the unique contribution that it makes to the understanding of communicative behavior. Existing methods of game theory analysis are heavily based in probability and simulation. In the second chapter a method for simplifying the modeling process for game theory interactions is presented. Specifically, the chapter discusses the development of equation-based, deterministic methods for calculating the outcomes of game theory interactions, rather than simulations. The third chapter describes a set of procedures for leveraging the simplified formulas elucidated in the second chapter for the purpose of simplifying the modeling of networked tournament interactions. These simplified network methods lead into a discussion in chapter four of the various network analysis tools and their uses in characterizing the network behavior of games. The discussion of these methods then proceeds into the presentation of a new type of ownership in networked tournaments, predicated on the idea that allowing partial node ownership may allow for the modeling of more advanced interactive behaviors, such as symbiosis. The discussion of partial ownership and co-extent strategies naturally lends itself to the processes defined in the fifth chapter. The fifth chapter is dedicated to the description of methods for classifying complex strategies using a consistent, procedural mechanism.