Master of Science (MS)
First Committee Member
Number of Pages
In the field of set theory, two-player infinite games of perfect information are well studied. The determinacy of various classes of such games have led to many important results. Furthermore, such determinacy follows from large cardinal axioms. In this thesis, we are instead interested in such infinite games with more than two players. With the study of two-player games being so fruitful, why aren't such infinite games studied with more than two players?;One difficulty in proving determinacy is that players need not play in any reasonable manner: A player may actually play a move that immediately results in a winning strategy or even an instant win for another player, even when such a move need not be played. We note that this leads to nondetermined games of extremely low complexity with three players, four players, five players, etc. However, we obtain determinacy of multiplayer games in which all but one player has an open payoff set and in which certain conditions are placed on certain player's moves: certain players will not be allowed to make a move that immediately results in a winning strategy for certain other players whenever such a move exists.
Determinacy; Games; Multiplayer
University of Nevada, Las Vegas
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McKenna, Christine Lee, "Determinacy and multiplayer games" (2005). UNLV Retrospective Theses & Dissertations. 1887.
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