Goshen College

Title: Fair Division and Cooperative Game Theory

Director(s): David Housman, Department of Mathematics and Computer Science

Email: dhousman@goshen.edu

Dates of Program: June 12 - August 5, 2005

Summary: By collaborating, several cities can save money on upgrading their water treatment facilities. What is a fair way of allocating the savings? Several people have inherited an estate, but they differ in their opinions about the worth of each item in the estate. What is a fair way of allocating the estate? Different sportswriters have different rankings for college football teams. What is a fair way of melding these different opinions into a single ranking ordering? In these situations, do the agents involved have incentives for stating their true costs, valuations, or rankings? In this research, students develop a mathematical model of a situation, define fairness properties, suggest allocation methods, and determine whether suggested allocation methods satisfy the defined fairness properties.

Student Researchers Supported by MAA:

• Elizabeth Adenegan, Hope College
• Jesus Medrano, Massachussets Institute of Technology
• Juan Mendez, Purdue University Calumet
• Nada Omer, Indiana University

Student Researchers Supported by Goshen College:

• Rozalia Tadjer, Goshen College

Program Contacts:

Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473

Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470

Support for NREUP is provided by the National Science Foundation's Division of Mathematical Sciences, the National Security Agency, and The Moody's Foundation.