Award Date

1-1-2005

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Derrick DuBose

Number of Pages

131

Abstract

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.

Keywords

Determinacy; Games; Multiplayer

Controlled Subject

Mathematics

File Format

pdf

File Size

3041.28 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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