AP Game Theory (sample article)

'NOTE: AP Game Theory does not actually exist (unfortunately). This is just a sample article.'

AP Game Theory is a one-term Advanced Placement class on introductory game theory. Game theory is a branch of applied mathematics concerned with analyzing and developing behavior in strategic situations, known as games, in which an individual's success in making choices depends on the choices of others. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the sports, and elsewhere. The class is taught solely by Mr. James Feery.

The College Board first administered AP Game Theory in 1999, soon after the introduction of AP Statistics. Enrollment for the AP Game Theory exam rapidly increased, faster than that of any other AP exam. At Stuyvesant, this is one of the most popular AP classes, rivaling even AP European History. This is likely a result of the shortness of the course and the exciting and widely applicable nature of game theory.

Curriculum
The first week is spent on the definition, components (players, utiles, and so forth), and basic applications of game theory. Then students move to the first unit, the language of games, which further lays the foundation for analyzing games by providing a means to transform them into diagrams known as matrices. The next unit develops rationality principles and the idea of responding to the other player's expected strategy. It also introduces graphs as a second method for analyzing games. The third unit introduces Nash equilibria, spending time on distinct examples, such as dating and Prisoner's Dilemma.

The course then shifts to studying series of multiple games. The fourth unit discusses mixed strategies and evolutionary stability. The next unit introduces sequential games, in which players move sequentially rather than simultaneously, and significant time is spent developing backward induction. The final unit before the AP exam analyzes situations in which some information is lacked. The discussion of imperfect information prompts a refinement of the notion of equilibrium into subgame perfect equilibrium. The unit also involves games in which one player knows something the other does not, a situation known as asymmetric equilibrium. After the AP exam, the class covers repeated games, studies strategies in game theory tournaments, and discusses the potential philosophical implications of the results of the tournaments.

Teaching style
Note: For a class with multiple teachers, this section would be divided into a subsection for each teacher.

Students generally find Mr. Feery's AP Game Theory class enjoyable due to his engaging personality, but hard because homeworks are long and tests are challenging. Mr. Feery is not generous with grades. The class provides students with a solid understanding of game theory and directly prepares them for the AP exam.

The class is mostly lecture-based with some discussion of the exercises and students' questions. It begins with a Do Now that either reviews the material of the day before or sets up the new topic with simple example. Meanwhile, Mr. Feery quickly checks the homework. After reviewing the difficult problems of the homework and the Do Now, he introduces a new topic or a new application of the most recent topic. Enough of the class is spent rationally developing each new topic, although not all theorems are rigorously proved. Significant time is spent understanding the use of behaviors and strategies in real-world situations such as Strategic Arms Limitation Talks, business partnerships, and soccer. Given that Mr. Feery doesn't finish the AP curriculum before the AP exam, which occurs before he reaches asymmetric equilibrium, some students feel that he spends too much time analyzing different applications of game theory. Most agree, however, that by Mr. Feery's instruction, they have a sound understanding of what they've covered.

Homework usually consists of several exercises from the textbook, reviewing what was learned that day. Since solutions usually require paragraph explanations, homework takes roughly 45 minutes. It is given every one or two days.

Tests consist of several questions, the difficulty of which is close to that of the more challenging problems on the homeworks, and beyond that of the majority of the AP exam. Mr. Feery's questions often require both deep analysis and substantial explanation. As a result, many students don't finish the tests. Mr. Feery rarely curves grades, but he lenient when deducting points. Also, he doesn't offer extra credit opportunities.

There is one project, which is the term paper, in which students analyze and discuss the game theory behind a political or economic event in the news. It requires 3–4 pages, although matrices and graphs cut down on the amount of writing needed.

Grading rubric
Report card grades strictly follow this rubric:
 * Tests &mdash; 60%
 * Homework &mdash; 15%
 * Classwork &mdash; 10%
 * Term paper &mdash; 15%

AP exam
The AP exam covers most of the curriculum, from the language of games to asymmetric information. It is considered one of the easier AP exams, since the material doesn't require much memorization, and there is only one term of material to recall. The exam consists of 50 multiple choice questions, eight short-answer questions, and four long-answer questions from which the student picks three. Most students find the short-answer section, which requires the most thought, to be the most time-pressed and therefore hardest. Regardless, most students at Stuyvesant get 5's.