Conflicting Goals: Competing Strategies
FYPR 004-02
MWF 11-11:50, 333 Swords Hall
Prof. David Damiano, 341 Swords Hall, 793-2476
e-mail: dbd@math.holycross.edu or
damiano@holycross.edu
Office Hours: MWF 10-11 AM and T 1-2 PM and by appt.
September 1, 1999
The Program
This year the First-Year Program (FYP) is shaped by the theme:
When self encounters other, how then shall we live?While the theme is intended to be a touchstone for the program, it is deliberately open to many interpretations. There is no single way to think about the theme, our relationship to it or how you and I might respond to it. Indeed, it is the hope of the FYP faculty that our understanding of the theme will evolve and deepen as we return to it throughout the year. The entire program can be seen as year-long conversation among the students and faculty. Its success, in large part, will be measured by our collective willingness to engage the theme through our common experiences. This requires that we be open to new ideas and fresh points of view at the same time that we develop our ability to think about them critically. This also holds true for the FYP faculty, since they are also engaging the theme and most of the common readings for the first time. The FYP seminars will enable us to address thematic questions from different discipline- based perspectives and, in turn, will give us an unusual opportunity to reflect on these disciplines from a broader perspective that transcends the traditional divisions between areas of knowledge.
The co-curricular component will consist of a variety of activities
that take place outside of class, including plays, concerts, lectures,
movies, field trips, and events and discussions in Hanselman, the
residence hall for all FYP students.
Conflicting Goals: Competing Strategies
The discipline-based work in this seminar concerns the branch of
mathematics known as game theory. Roughly speaking, game theory is a
collection of algebraic methods for the analysis of transactions
between two or more players in a game. A game could be a game in
the everyday sense of board games or card games, but it is more likely
to be a situation in which the players have a short list of strategies
that they pursue to obtain a goal. For example, the players might be
two companies competing to control a market for a product that each
manufactures. Each company might have to choose among several
strategies, but the outcome is determined by the combined effects of
the chosen strategies on the market.
In the first semester we will consider two different categories of
games. First we will consider zero-sum games. These are games
in which the interests of the players are strictly opposed so that the
payoff to the winner is equal to the loss of the opponent. These
games might be considered as models of situations of pure conflict.
Later in the semester we will consider more complicated games in which
the payoffs and losses for outcomes do not add to zero. These games
are called non-zero-sum games. As we analyze these games we
will have to consider whether each player will work simply for their
own best outcome or whether cooperation between the players would
allow for a better common solution.
Since the initial mathematical development of game theory in the
1940's and early 1950's, it has been applied in an array of
disciplines, including anthropology, biology, economics, philosophy,
political science, psychology, and sociology. Indeed, claims have
been made for the ability of game theory to explain a bewildering
variety of activities and behaviors. We will spend time this
semester investigating some of these claims with goal of deciding for
ourselves what we can learn from applying game theory to interactions
between self and other.
The Classroom
In addition to lectures, we will have discussions involving the entire
class, and we will regularly break up into assigned groups of 3-4
students and use a ``small group'' discussion format. The primary
goals of these sessions are to have more people actively involved in
the discussion and to promote peer learning. We will often take a
``discovery'' approach rather than a traditional ``lecture/read the
text'' approach. It will be important for us to free ourselves from
the constraints imposed by thinking of mathematical problems as things
to do after reading a section of a text or attending a lecture. Both
the general emphasis on discussion and the particular emphasis on the
discovery method mean that you will have ample opportunity to be
active participants in the class and, more importantly, in developing
your own understanding and insights into the subject matter.
FYP Journals
As part of the course requirements, you will have to keep an academic
journal. This is not a personal diary or log of classroom activities,
but rather a place for you to reflect on discussions and activities
related to the program or current events on and off campus in light of
the program. You might use it to continue a discussion we began in
class, to react to a lecture or film you saw, in connection with the
program or in another context, or to make connections between the
class material and material from other classes. You should think of
this as a public document, which I will be reading and which you
should be willing to show to members of the class. I will often
suggest topics for journal entries. In addition, you will be required
to write entries on a number of the common events, which will be
determined as the semester progresses. As a general rule, you must
make at least two journal entries each week. I will collect the
journals once a week, usually on Fridays, and will make written
comments and pose questions for further thought. I will be reading
your journals for content and not style. Nonetheless, you should take
care with your writing as others will be reading it on occasion. An
overall evaluation of your journal will be part of your final grade,
but I will not grade individual entries.
Assignments and Grading
There will be four types of regular assignments during the semester,
the FYP journals (described above), 2 papers of 3-5 pages concerning
the common readings (due Friday, September 17 and Monday, October 18),
individual game theory assignments, and collaborative game theory
assignments based upon the small-group work in class. There will also
be an in-class mid-term exam in on Monday, October 4 and take-home
final exam during the exam period. The format of the final exam will
be announced later in the semester.
Note that the Class Participation component includes attendance at
co-curricular events. There will be an average of one event per week.
It is strongly recommended that you attend as many of the events as
possible. Attendance is mandatory at the events that are central to
the program or to this class. The co-curricular events will be
discussed in class. A list of events that have been scheduled is
given at the end of the syllabus.
Grading Scheme:Texts:
The following texts are required texts for the first semester. These are available in the College Bookstore in the Hogan Campus Center. Additional material will placed on reserve in the Science Library on the first floor of Swords Hall.
Common Readings:Texts for Conflicting Goals: Competing Strategies:
- Bone. Fae Myenne Ng. Harperperennial 1993.
- Narrative of the Life of Frederick Douglass: An American Slave, Written by Himself. Frederick Douglass. Ed. David W. Blight. Bedford Books 1993.
- Course Packet of writings by and about Frederick Douglass.
- Economic and Philosophic Manuscripts of 1844. Karl Marx in The Marx-Engels Reader 2nd Edition, Ed. Robert C.Tucker.
- The Tempest. William Shakespeare. Signet Classic Edition, 1998.
- Game Theory and Strategy. Philip D. Straffin. The Mathematical Association of America, 1993.
- Moral Calculations: Game Theory, Logic, and Human Frailty. László Méro. Springer-Verlag 1998.
Schedule of Readings
The common texts should be read by the first day they are discussed in class. Particular readings in Straffin and Méro will be assigned weekly.
Schedule of Events and Activities as of September 1: