Course Outline of Record

Item	Value
Eff Term	Fall 2026
Curriculum Committee Approval Date	12/02/2025
Top Code	220400 - Economics
Units	3 Total Units (Lecture Units 3)
Hours	54 Total Hours (Lecture Hours 54)
Total Outside of Class Hours	108
Total Student Learning Hours	162
Course Credit Status	Credit: Degree Applicable (D)
Material Fee	No
Basic Skills	Not Basic Skills (N)
Repeatable	No
Open Entry/Open Exit	No
Grading Policy	Standard Letter (S),  Pass/No Pass (B)
Local General Education (GE)	Area 2 Mathematics (GB2)

Course Description

Formerly: Game Theory. This course provides an introduction to the mathematics of game theory. The course will use mathematical techniques and probabilities to calculate game strategies and interactions between rational decision makers. It will apply statistics to analyze and maximize outcomes of multiplayer games. The course will build game theory frameworks including Prisoner's Dilemma, games of chance, strategic games, and real world applications of market competition and international relations. PREREQUISITE: Course taught at the level of intermediate algebra or appropriate math placement. Transfer Credit: CSU; UC.

Course Level Student Learning Outcome(s)

1. Solve linear systems for mixed strategy probabilities.
2. Use game matrices and game trees to solve for optimal decisions of multiplayer games.
3. Apply game theory strategies to real world decision making.

Course Objectives

• Describe mathematical techniques used in game theory decision making.
• Use algebraic techniques, including linear models and systems of equations.
• Solve for the probability and expected value of outcomes.
• Analyze quantitative solutions in game strategizes to solve for the maximized outcome.
• Identify strategies and equilibrium in game theory matrices.
• Describe players and payoffs in vectors.
• Solve zero-sum and non-zero-sum games for optimal strategies and equilibrium.
• Calculate the expected value of mixed strategy games and solve for the optimal strategy.
• Transform matrices to extensive form game trees.
• Apply backward induction to solve for Subgame Perfect Nash Equilibrium in sequential games.
• Apply the fixed point theorem in the proof of the existence of Nash equilibrium.
• Apply quantitative analysis to a designed experiment that compares summary statistics on a compiled data set to calculated probable outcomes.

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Lecture Content

1. Game Matrices and Payoff Vectors
   1. Players
   2. Matrices
      1. 2x2 games
      2. 2x3 games
      3. Larger matrices
      4. Symmetric versus asymmetric
   3. Compute Payoff Matrices
      1. Evaluate numerical options to determine payoffs in a matrix
         1. Calculate probabilities of outcomes
         2. Calculate all possible outcomes
      2. Payoffs: u_i>0, u_ii=0
2. Sets, Probability, and Expected Values
   1. Sets and subsets of decisions
      1. Evaluate elements in sets
         1. AuB, A∩B
         2. Subsets
      2. Combinations
         1. Solve for the number of combinations of n taken r at a time: nCr=n!/r!(n-r)! 
      3. Permutations
         1. Solve for the number of permutations of n taken r at a time: nPr=n!/(n-r)!
   2. Trees/Extensive Form Games
      1. Decision nodes
         1. Calculate the number of possible outcomes in a decision tree
         2. Solve for the expected probability of each outcome: P(x)=n(E)/n(S)
         3. Compare the quantitative outcomes at each node of the decision tree to solve for the optimal strategy
      2. Subgames
   3. Games of Chance
      1. Solve for the probability of outcomes and the expected value of payoff: EV=ΣP(x)x
      2. Game applications
         1. Rolling dice
         2. Roulette
         3. Poker
      3. Compare actual outcomes to expected outcomes as sample size increases
3. Perfect Information
   1. Preferences with uncertain outcomes
4. Equilibrium
   1. Nash/Best Response
      1. Solve for the best response of each player against other players simultaneously
      2. Maximize gains of player i|all other players
      3. Strategy profile s for every player i: u_i(s_i,s_-i)≥u_i(s'_i,s_-i)
      4. Fixed point theorem 
   2. Bayesian
      1. Conditional probability of event X based on occurrence of event Y
      2. Bayes Theorem: P(X|Y)=(P(Y|X)P(X))/(P(Y))
   3. Pair
   4. Deadlock
   5. Selten/subgame perfect
5. Strategies
   1. Pure
      1. Zero randomization
   2. Dominant
      1. Strictly dominant
         1. u_i(σ_i,s_-i)>u_i(s_i,s_-i)
      2. Weakly dominant
   3. Mixed
      1. Equations of expected value using payoff matrix
         1. Unknown variables
         2. Algebraic substitution
      2. Mixed strategy algorithm
      3. Probability of mixed strategy
      4. Efficiency
6. Graphical Solutions
   1. Equation of a Line: y=mx+b
   2. Systems of Equations
   3. Algebraic Substitution
7. Types of Games
   1. Zero-sum games
   2. Non-zero sum games
   3. Discrete game  
   4. Continuous rounds
   5. Simultaneous decisions
   6. Sequential decisions
      1. First move advantage
8. Iterated Elimination 
9. Backward Induction
   1. Analyze numerical payoffs of a game from back to front
   2. Calculate possible outcomes of decision tree nodes
   3. Analyze quantitative outcomes to describe the optimal strategy at each node of a decision tree
   4. Solve for the optimal opening strategy that maximizes expected gains for each player
   5. Solve for equilibrium
10. Prisoner's Dilemma
    1. Cooperation
    2. Tit for Tat
    3. Nash equilibrium: σ*=((0,1),(0,1))
11. Sample Games
    1. Matching Pennies
    2. Chicken
    3. Tic Tac Toe
    4. Rock-Paper-Scissors
    5. Second price auction
12. Applications
    1. Price fixing
    2. Price wars
    3. Duopolistic competition
    4. Quid pro quo
    5. International trade and tariffs
    6. Arms races/escalation
    7. Mechanism design

Method(s) of Instruction

• Lecture (02)
• DE Live Online Lecture (02S)
• DE Online Lecture (02X)

Instructional Techniques

-

Reading Assignments

Textbook Online readings and supplemental materials to apply game theory principles

Writing Assignments

Problem solving exercises related to game theory applications and decisions Written solutions to homework problems Students will calculate and solve math problems related to games, and decision making strategy Use statistical techniques including probability and expected value to solve for maximize outcomes for game strategies.

Out-of-class Assignments

Written solutions to homework, quiz, and test problems. Quantitative analysis of mathematical problem solving including an analysis of the outcomes.

Study Non-Contact Hours Recommended

108

Methods of Student Evaluation

• Midterm Exam
• Final Exam
• Written Assignments
• Projects (Individual/Group)
• Problem Solving Exercises

Demonstration of Critical Thinking

Solve game theory matrices for optimal responses and equilibrium. Calculate probabilities of mixed strategy games and evaluate quantitative outcomes of actual and expected values. Apply game theory to political and economic scenarios and games of chance. Compare quantitative outcomes of various strategies to explain the optimal decision for players. Students will design an experiment and perform quantitative analysis (QA) on a created data set by calculating summary statistics on observed numerical outcomes and comparing to calculated expected values. One element of the experiment should compare the effect of various sample sizes on actual versus calculated probabilities the to prove convergence when sample size increases. The experiment should also compare and contrast the effect of an increase in combinations on actual versus probable outcomes and divergence from calculated expected value when the number of outcome combinations increases.

Required Writing, Problem Solving, Skills Demonstration

Calculate payoffs and determine strategies for solving games. Convert payoff matrix information into extensive form game trees for decision making. Apply algebraic techniques to solving game theory equation systems. Use statistical techniques to solve and analyze game strategies including comparing calculated expected value to actual values. Demonstrate that forward induction and backward induction in evaluating quantitative outcomes at each node of a decision tree lead to the same result.

Resources Subscreen

• Textbook: Nordstrom, J.. Introduction to Game Theory: a Discovery Approach (Classic). Jennifer Firkins Nordstrom (OER) (2020).
• Textbook: Bonanno, G.. Game Theory. Giacomo Bonanno (OER) (2024).
• Textbook: Spaniel, W.. Game Theory 101: The Complete Textbook (Classic). William Spaniel (2020).
• Textbook: Faigle, Ulrich. Mathematical Game Theory. World Scientific Publishing (2022).
• Textbook: Illowsky, B., Dean, S., et. al.. Introductory Statistics. OpenStax (OER) (2023).
• Textbook: Sekhon, R. . Applied Finite Mathematics (Classic). OpenStax (OER) (2011).

Eligible Discipline(s)

• Mathematics: Master’s degree in mathematics or applied mathematics OR bachelor’s degree in either of the above AND master’s degree in statistics, physics, or mathematics education OR the equivalent. Master's degree required.
• Economics: Master’s degree in economics OR bachelor’s degree in economics AND master’s degree in business, business administration, business management, business education, finance, or political science OR the equivalent. Master's degree required.