I. Number and title of course

Math 304 Games and Linear Programming

A. To provide an elementary introduction to the important ideas and techniques of the theory of games and linear programming for which all students at our college would be eligible.

B. To provide a fundamental and basic course which would be useful to students majoring in many different disciplines and having varied career interests.

A. To present in a clear, elementary fashion some of the ideas and problems in the areas of game strategies and optimization.

B. To offer college students majoring in diverse areas an introduction to the use of elementary mathematical methods in finding optimal choices in business, industry, economics, medicine, social sciences, behavioral sciences, and biological sciences.

A. To help the students develop techniques in line graphing.

B. To facilitate the solution of inequalities.

C. To utilize linear graphs in finding optimal choices.

D. To help students gain facility in addition and multiplication of matrices.

E. To introduce the student to computing determinants and solving systems of equations.

F. To use matrices and randomization in solving for game strategies.

G. To tie in the relationships between the theory of games and linear programming.

A. Linear Programming: A Geometric Approach

1. Linear statements

2. Linear inequalities

3. The linear programming model

4. Graphing straight lines

5. Solving systems of equations

6. Von Neumann Minimax theorem

B. Matrix Algebra

1. Vectors and Matrices

2. Matrix addition and multiplication

3. Determinants; Cramer's Rule

4. Gaussian elimination

5. Finding inverses

C. Game Theory

1. Payoff matrices

2. Saddle-point games; pure strategies

3. Dominance

4. Non-strictly determined games; randomized or mixed strategies.

5. Oddment Principle

6. 2xm and mx2 games; trial and error

7. 2xm and mx2 games; graphical method

8. mxn games; subgames

D. Linear Programming: The Simplex Method

1. Slack variables

2. The simplex tableau

3. Pivotal elimination

4. Basic feasible solutions

5. Relationships between game theory and linear programming

1. Buckler, I. and Nutine, H., Game Theory in the, 1969. Behavioral Sciences, Pittsburgh: University of Pennsylvania Press

2. Chernoff, H. and Moses, L.E., Elementary Decision Theory, New York: Wiley, 1959.

3. Cooper, L. and Steinberg, D., Methods and Applications of Linear Programming,Philadelphia: W.B. Saunders, Co., 1974.

4. Dortmann, R., Application of the Simplex Method to a Game Theory Problem, Cowels Commission for Research in Economics, Monograph 13, John Wiley, 1947.

5. Dresher, Mr., Games and Strategy: Theory and Applications, Englewood Cliffs: Prentice?Hall, 19 1.

6. Dresher, Mr., Methods of Solution in Game Theory, Econometrica, Vol. Id, 1950.

7. Gass, S.I., Linear Programming, 4th edition, New York: McGraw?Hill, 1975.

8. Huff, D., How to Take a Chance, New York: W.W.Norton, 1959.

9. Luce, ?R.D. and Ralffa, H., Games and Decisions, New York, J. Wiley, 1957.
 
 

Ap

May 10, 1984