Abbreviated Game Theory Lesson

Context Summary

Contextually the students have been studying Game Theory. The understand the definition of a game. They have learned what a 2-person zero sum and non-zero sum game is. They will have learned how a game can be represented with a matrix along with payouts. Finally, the students will have learned what a 'strategy' is and how one can be dominant. Lessons after this reading will focus on Nash-Equilibria and how it is applied to Prisoner's Dilemma. The students will then look at other modern day examples where game theory can be useful. Game theory is a sub field of mathematics and the reading is designed for high school students.

Reading Summary

The article discusses the game theoretical situation called “Prisoner's Dilemma”. It is when two members of a criminal gang are arrested. The members must decide if they are going to “snitch” on their partner or remain silent. Each of the 4 possible scenarios result in different amounts of jail time for the criminals. The situation can be modeled by a matrix with different pay outs. The article discusses the confusing result that occurs when each players play “rationally”. The article then goes on to talk about extended “iterated” versions of the game where the game is played over and over between the same prisoners. After that the article discusses the tournaments that sprang from this iterated version of Prisoner's Dilemma.

Citation: Prisoner's Dilemma. In Wikipedia. Retrieved July 29^th, 2014, from http://en.wikipedia.org/wiki/Prisoner's_dilemma

Flesch-Kincaid GradeLevel: 16.3

Prisoner's Dilemma Lesson Plan

2 mins

-Warmup: What is the difference between and zero-sum and non-zero some game?

20 mins

-Introduce Prisoner's Dilemma situation.

-Ask students how they would play the game

-Let students play the game with one partner

-Show the students that rational play and the idea of dominance leads both players to betray

10 minutes

-Introduce the idea of playing many consecutive rounds of the game

-Ask students what they think a good strategy might be like

-With the same partner let the students play a 10-iteration game of prisoner's dilemma

25 minutes

-Introduce the idea of playing multiple iterations with multiple pairs of partners

-Have students break into groups of 3 and play a round robin game of prisoner's dilemma with 10-iteration games

-Ask which students ending up with the highest score (lowest amount of jail time)

-Ask why students chose their strategy

-Introduce idea of cooperation