{"@context":"http://iiif.io/api/presentation/2/context.json","@type":"sc:Manifest","@id":"https://iiif.quartexcollections.com/wesleyan/iiif/638d2468-b1ec-45f8-b96f-d0aeecef630f/manifest","label":"m2022-s525","metadata":[{"label":"Title","value":"The Grossone methodology: applications in non-Archimedean game theory and linear programming"},{"label":"Subject","value":["Linear programming","Game theory"]},{"label":"Rights","value":["In Copyright"]},{"label":"Repository","value":["University Archives"]},{"label":"Language","value":["English"]},{"label":"Item Information","value":"<a href=\"https://onesearch.wesleyan.edu/permalink/01CTW_WU/12cbh08/alma9933037248703768\" target=\"_blank\">M2022 S525</a>"},{"label":"Held By","value":"Wesleyan University Library, Wesleyan University, Middletown, CT, USA"},{"label":"Group","value":["Theses & Dissertations"]},{"label":"Name(s)","value":["Shah, Dhhyey Beej (creator)"]},{"label":"Administrative Note","value":"Node ID: 17174<br>Author Contact: dshah@wesleyan.edu<br>Local Identifier: 981.pdf<br>PID: ir:3275"},{"label":"Author-supplied Keywords","value":["Non-Archimedean","Linear programming","Game theory","Grossone"]},{"label":"Degree","value":["Master of Arts"]},{"label":"Description","value":"<p>This thesis focuses on examining Game Theory and its intersection with Linear Programming, with the hopes of using a relatively new tool, the grossone methodology, to analyze and solve non-Archimedean games. We first discuss some basic game-theoretic concepts and show how linear programs can be used to solve two-player zero-sum games. We then introduce and prove the Fourier-Motzkin elimination algorithm and a couple of forms of the Farkas Lemma, which are tests of feasibility of linear programs, with the hopes of further extending these results to non-Archimedean cases. We then survey the grossone methodology, which is closely related to nonstandard analysis, and the grossone-based positional numeral system; these are the tools we wish to use to model our non-Archimedean cases. We conduct an experiment to analyze and explore the merits and drawbacks of the grossone methodology. Lastly, we discuss the hurdles in the way of extending the aforementioned tests of feasibility of linear programs to the grossone case. 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