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  • Brams' Theory of Moves and the Dynamic Aspects of Game Theory

    Description:
    Game theory is used in a wide variety of applications. It is most notably used in economics but also has widespread applications in politics and biology. In this paper, we will only look at the economic and political applications of game theory in general and Steven J. Brams’ Theory of Moves (TOM) in particular. Brams uses numerous examples from politics, economics, and religion to illustrate the compatibility of TOM in real life issues as compared to the standard game theory. We will refer to these examples when appropriate. In the succeeding paragraphs and in other sections of this paper, we discuss how game theory, especially in its dynamic form, can be used to model real life situations.
    Subject:
    Mathematics
    Creator:
    Adhikari, Samik
    Contributor:
    Dr. Brian Hopkins, Thesis Advisor
    Owner:
    lsquillante@saintpeters.edu
    Publisher:
    Saint Peter's University
    Date Uploaded:
    10/20/2020
    Date Modified:
    10/20/2020
    Date Created:
    Spring 2011
    Rights Statement:
    In Copyright
    Resource Type:
    Research Paper

  • God's Number and the Robotic Turn Metric

    Description:
    Since the invention of the Rubik’s cube in the 1970s, mathematicians have been captivated with finding out the maximum number of moves needed to solve the Rubik’s cube optimally from any of the cube’s approximately 43 trillion possible positions. This value, known as God’s number, depends on the metric, which is the set of allowed moves. This thesis proposes a new “robotic turn metric” based on allowing antipodal faces of the cube to be turned simultaneously. Although human solvers cannot easily accomplish such moves, they are used by various robotic cube solvers, thus the name. We explore lower and upper bounds for God’s number in this metric and how it compares to God’s number in the Face Turn Metric and Quarter Turn Metric.
    Subject:
    Mathematics
    Creator:
    Hollingsworth, Nykosi
    Contributor:
    Dr. Brian Hopkins, Thesis Advisor
    Owner:
    lsquillante@saintpeters.edu
    Publisher:
    Saint Peter's University
    Date Uploaded:
    10/14/2020
    Date Modified:
    10/14/2020
    Date Created:
    April 28, 2015
    Rights Statement:
    In Copyright
    Resource Type:
    Research Paper

  • ON THE DISJUNCTIVE RADO NUMBER OF THE EQUATIONS ax1 = x2 AND bx1 + x2 = x3

    Description:
    For a given system of linear equations L, the Rado number of the system is the least integer n for which every t-coloring of {1,...,n} contains a monochromatic solution of one of the equations in L, if such an integer exists. In this thesis, the 2-color disjunctive Rado numbers for the equations ax1 = x2 and bx1 + x2 = x3 are determined for more than half of all values of a and b.
    Subject:
    Mathematics
    Creator:
    Purcilly, Adam
    Contributor:
    Dr. Brian Hopkins, Thesis Advisor
    Owner:
    lsquillante@saintpeters.edu
    Publisher:
    Saint Peter's University
    Date Uploaded:
    10/14/2020
    Date Modified:
    10/14/2020
    Date Created:
    Spring 2013
    Rights Statement:
    In Copyright
    Resource Type:
    Research Paper

  • When Prisoners Enter Battle: Natural Connections in 2x2 Symmetric Games

    Description:
    Recently, game theory has gained much interest from many mathematicians as well as economists and psychologists. The simplest and most popular games studied in this field are the 2 X 2 games, which involve two players with two different choices each; each player makes his or her decision individually, but his or her choice will affect the outcome for both that player as well as for the other player. Within these 2 X 2 games, each player has his or her own preference in terms of what outcomes are best for them; for each of the four possible outcomes in these 2 X 2 games, each player also receives a certain payoff, which could be a good or bad payoff. If both players have the same ordering of outcomes, then the game is called symmetric, meaning if the players were switched, the outcomes would be in the same order as initially. In this paper, I show the results I found while researching the connections between these symmetric 2 X 2 games. The twelve total symmetric 2 X 2 games can be shown on a 2D x-y axis; these games can be separated into six different sectors. In each section, the games involved can be manipulated, when transitioning to another game with different payoff preferences, to one common game. When one game is changed to another by simply swapping two of the payoffs, a transition game in between these games appears; by doing a simple operation to these transition games, I was able to find one universal game in each sector. This proves that these are more closely related than mathematicians previously believed. If one has an interest in game theory, wants to learn about an interesting topic in mathematics, or just wants to see what one can do with the power of mathematics, one can read all about the 2 X 2 symmetric games in When Prisoners Enter Battle: Natural Connections in 2 X 2 Symmetric Games.
    Subject:
    Mathematics
    Creator:
    Heilig, Sarah
    Contributor:
    Dr. Brian Hopkins, Thesis Advisor
    Owner:
    lsquillante@saintpeters.edu
    Publisher:
    Saint Peter's University
    Date Uploaded:
    10/14/2020
    Date Modified:
    10/14/2020
    Date Created:
    March 28, 2011
    Rights Statement:
    In Copyright
    Resource Type:
    Research Paper

  • Enumeration of Austrian Solitaire

    Description:
    This thesis concerns a variant of Bulgarian Solitaire, called Austrian solitaire, introduced by Akin and Davis. A primary result is the derivation of a formula for the number of states under Austrian Solitaire. This thesis characterizes the Garden of Eden states. The thesis also gives a possible characterization for the fixed points and examines other cycle states with various conclusions.
    Subject:
    Mathematics
    Creator:
    Bastola, Kapil
    Contributor:
    Dr. Brian Hopkins, Thesis Advisor
    Owner:
    lsquillante@saintpeters.edu
    Publisher:
    Saint Peter's University
    Date Uploaded:
    10/14/2020
    Date Modified:
    10/14/2020
    Date Created:
    Fall 2012
    Rights Statement:
    In Copyright
    Resource Type:
    Research Paper

  • Characterizing Cycle Partition in 2-Row Bulgarian Solitaire

    Description:
    This paper studies cyclic partitions under the operation 2-row Bulgarian solitaire. We develop tools such as block notation to make characterizing cyclic partitions easier. Using these blocks, we see that cyclic partition under 2-row Bulgarian solitaire have independently cycling diagonals satisfying one of four conditions. We conclude with an enumeration results that allow us to calculate the number of cyclic partitions for a given integer n.
    Creator:
    Pradhan, Sabin
    Contributor:
    Dr. Brian Hopkins, Thesis Advisor
    Owner:
    lsquillante@saintpeters.edu
    Publisher:
    Saint Peter's University
    Date Uploaded:
    10/23/2019
    Date Modified:
    10/23/2019
    Date Created:
    May 2016
    Rights Statement:
    In Copyright
    Resource Type:
    Research Paper