Index

Discrete Mathematics Project

Matrices Activity

Title

Pizza Wars (Greta Lawlor)

Goals

1) Students will explore game theory through the use of a matrix.

2) Students will identify the best strategy for the players in Pizza Wars.

3) Students will work in groups to arrive at the best strategies and be able to explain and justify their solution to the class.

Abstract

This activity asks students to determine the best strategy for two pizza parlor owners giving away cheese pizza with or without pepperoni in a pizza war. The students will set up a matrix to help them determine which strategy is best for each owner.

Problem Statement

Review with students the set up of a matrix and discuss how to set up the rows and columns. Remind them that there will be several strategies, but they are to choose the best for each of the pizza parlor owners. Identifying strategies and choosing the best strategy is the central theme.

Instructor Suggestions

1) Review matrices, rows, columns and how to set up a game matrix.

2) Hand out "Pizza Wars." Have the students read it individually and then work together in their groups to find the best strategies for each player.

3) When the groups are finished, have a spokesperson from each group present their solution. If several of the solutions are essentially the same, only have those that are different present.

4) Discuss the students work, and resolve any disagreements among the group.

Materials

"Pizza War" activity sheet, transparencies, marker.

Time

Review and introduction to problem (10 minutes), individual work (5 minutes), group work (20 minutes), presentations (20 minutes)

Mathematics Concepts

Discrete Mathematics Concepts

Game Theory - zero sum games

Related Mathematics Concepts

Matrices, percentage, matrix multiplication

Problem Solving, Communication, Reasoning, Connections, Discrete Mathematics

Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity could be integrated into Algebra or Geometry under the topic of matrices and their related operations. It could also be introduced in a probability/statistics class or unit when focusing on expected value.

Further Investigation

Students could expand the problem to more parlor owners or they could extend the same ideas to non-zero sum games. Software available as a tool for the students is EXPECTATION and GAMES.