Survey of results in impartial combinatorial games and an extension to three-player game
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There are several known methods to find winning strategies for two-player combinatorial games. This thesis surveys results known for two-player combinatorial games and elucidates a particular winning strategy for a three player game using graph theory. The motivation for work in this area is a belief on the ability of graph theoretic tools to handle multi-player combinatorial game analyses. A winning strategy for two-player undirected vertex Geography game has been formulated earlier and has been shown to be polynomial time. This thesis extends the result to three-player undirected vertex Geography, played on directed trees and answers the question "Does the first player have a winning strategy?". The extension serves as a platform for generalizing results to games involving more than three players.
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Venkataraman, Sripriya. "Survey of results in impartial combinatorial games and an extension to three-player game." (2001) Master’s Thesis, Rice University. https://hdl.handle.net/1911/17477.