Pizza Wars (Greta Lawlor)
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.
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.
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.
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.
"Pizza War" activity sheet, transparencies, marker.
Review and introduction to problem (10 minutes), individual work (5 minutes), group work (20 minutes), presentations (20 minutes)
Discrete Mathematics Concepts
Game Theory - zero sum games
Related Mathematics Concepts
Matrices, percentage, matrix multiplication
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Discrete Mathematics
Colorado Model Content Standards
Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
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.
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.
This activity should be used as an early activity in the unit. More difficult problems can be solved by building off of this problem. There are other gaming strategies, for instance, games based on a 3 X 3 magic square. This would be a great extension, especially when working on developing strategies. To find information on games based on a 3X3 magic square, consult aha! Insight by Martin Gardner (page 115.)
Gardner, Martin. aha! Insight. 1978. New York: W. H. Freeman and Company.
Kenney, M. J., & Hirsch, C. R. (Eds.) (1991). Discrete Mathematics Across the Curriculum, K-12. Reston, VA: National Council of Teachers of Mathematics.