Sep 26, 2023
MATH 1250 - Introductory Game Theory
The course introduces mathematical models for situations of conflict, whether actual or recreational, and considers two-person, n-person, zero-sum and nonzero-sum games, Nash equilibria, cooperation and the prisoner’s dilemma. Application to fields such as environmental policy, business decisions, football, evolution, warfare and poker will be analyzed. The course uses elements of algebra, geometry and probability skills, including matrix manipulation, linear and quadratic equations, graphing equations, extracting information from graphs, determining probabilities and expectation values.
Requisites: C or better in MATH D004 or MATH D005 or MATH 102 or Math Placement Level 1 or higher
Credit Hours: 3
General Education Code: 1M
Repeat/Retake Information: May be retaken two times excluding withdrawals, but only last course taken counts.
Lecture/Lab Hours: 3.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
- Calculate Nash Equilibria in non-zero-sum games and identify stability and Pareto optimality of solutions.
- Calculate outcomes and find winning strategies in simple combinatorial games.
- Find dominance, saddle-points and mixed strategies for zero-sum and interpret their meanings in applications.
- Model games by game trees and calculate expected payoffs for branches.
- Model two entity conflicts, both zero- and non-zero-sum, as matrix games.
- Recognize game theory as a mathematical tool that is applicable in a large variety of contexts.
- Understand that non-linear problems can have surprising consequences, such as random winning strategies, existence of multiple solutions, and non-existence of acceptable solutions.
- Use linear equations, quadratic equations, and their graphs.
- Use the basic axioms and methods of discrete probability.
- Verify/disprove the axioms of utility and fairness in matrix games.
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