Undergraduate Research Mentored by David Housman

Paper titles with links are available for download; other papers can be obtained by contacting me. These papers are the product of an eight week summer program, academic year thesis, or a 1-3 credit course term paper. Although there are lots of great ideas here, do not expect polished work.

Year & Type Student Name Paper Title
1986 MQP Anzivino, Anthony Worcester Family Health and Social Service Center Schedule Optimization
1986 IQP Bennett, Dana WPI Scheduling as an Allocation Problem
1987 MQP Day, Wayne Numerical Solutions of Implicit Differential Equations
1987 IQP

Hallisey, John
Rudy, Scott
Zapatka, Mark

The Role of Information in Offshore Oil Lease Bidding
1988 WREU Brown, Donna
Jew, Lori
Macdonald, Diane
The Name of the Game
1988 WREU Brown, Donna Cooperative Games on Weighted Graphs
1989 MQP Cortese, Susan
Menard, Christopher
Competitive Bidding Strategies for Off-shore Oil Lease Auctions
1989 MQP Deligiannides, Hariton
Nelson, Mark
Coal Shipping Expert System
1989 MQP Ferreira, Mary Frances Multiattribute Utility Function for a Group of Experts
1989 IQP French, Jonathan Coal Shipping Expert System
1989 IQP Harrell, Peter Social Choice Reversal Paradoxes
1989 MQP Jew, Lori Properties of Allocation Methods
1989 MQP Reed, Leslie Computational Methods for the Nucleolus
1989 WREU Martell, Christine
Winn, Holly
Monotonicity of Values for Cooperative Games
1990 DREU Chen, Cheng-Jih Characterization of the Shapley-Shubik and Banzhaf Power Indices with Transfer and Fairness Axioms
1990 DREU Chiu, Tien-Yee Cooperative Games: Cliques in Graphs
1990 DREU Grande, Kathryn Jane Reasonableness, Monotonicity and Rationality
1990 DREU Letscher, David The Shapley Value on Partially Defined Games
1990 DREU Maltenfort, Michael An Allocation Method from Individual Compaint Functions
1990 DREU Maltenfort, Michael Consistency on Partitition Form Games
1990 DREU McCaulley, Patrice Axioms and Values on Partition Function Form Games
1991 DREU Arthur, Daniel Oligopoly in Partition Function Form
1991 DREU Merki, Stephanie Values on Partition Function Form Games
1991 DREU Patashnick, Owen Consistency: An Axiomatic Classification of Allocation Methods on TU Characteristic Function Form Games
1991 DREU Saraniti, Brett Intergenerational Games
1991 DREU Ventrudo, Tom
Wallman, Jodi
Finding a Value on Partially Defined Games
1992 DREU Baldan, John Properties of Simple Games
1992 DREU Brennan, Carol
Morrill, Mary Dana
Spanning Forest Games
1992 DREU Lee, Roger A Characterization of the Extreme Monotonic Extensions of a Partially Defined Game
1992 DREU Lee, Roger Some Observations on a Notion of Consistency
1992 DREU Lim, Darren Forest-Size Games
1992 DREU Pinzon, Luz Cooperative Games in Partition Function Form
1993 Rutgers Pinzon, Luz Reasonable Allocations for Cooperative Games
1993 DREU Howes, Jennifer The Nucleolus and Shapley Value for Cooperative Matching Games on Weighted Graphs
1993 DREU Rich, Jennifer The Shapley Value and Partially Defined Games
1993 DREU Theoharidis, Maria The Shapley Value for Partition Function Form Games
1994 Allegheny O'Toole, Kathy ABACUS: A Staffing Model Implemented by Chubb & Son Insurance
1994 HHMI Brutt, LeeAnne A Value for Zero-Monotonic Partially Defined Games
1995 Allegheny Link, Catherine  
1997 Allegheny Johnson, Jennifer Maximal Flow Problems and Cooperative Games
1997 Allegheny Timcho, Jennifer Auctions
1999 Maple Engelsone, Anna Central Extensions of Partially Defined Games (Maple Appendix)
2000 Maple Hilman, Reynard Fair Allocation Method for Steiner Tree Networks
2000 MA300 Amstutz, Sarah Menelaus Theorem
2000 MA300 Schrock, Matthew Sprouts: More Than Vegetables
2001 Goshen Engelsone, Anna Central Extensions of Partially Defined Games (Maple Appendix)
2001 Maple Amstutz, Sarah Fair Division
2001 MA300 Histand, Andrew Stable Forms in the Game of Life on a 3 by n Torus
2001 MA300 Soe, Htun Perfect Numbers and Perfect Squares
2002 MA300 Ramer, Chellie The Non-Planarity of the Lattice Diagram of the Natural Numbers Under the Relation Divides
2003 Maple Histand, Andrew The Range Nucleolus for Cooperative Games
2003 Maple Ramer, Rachelle Convexity of Partially Defined Cooperative Games
2003 MAA Abebe, Kaleab A Maximally Equitable Solution in Fair Division with n Players
2003 MA300 Bauman, Matthew Leftist Numbers
2003 MA300 Henn, Rebekah The Island of Truthtellers and Liars
2003 MA300 Nafziger, Rosanna Folding Papers and Planes: A Critical Difference
2004 Goshen Ramer, Rachelle Convexity of Partially Defined Cooperative Games
2004 MAA Huang, Jiayun (Aeron) Graphical Approach and Property Tests in Fair Division Problems with Indivisible Objects and Monetary Compensation
2004 MAA Johnson, Jesse Envy-Free and Efficient Allocations
2004 MAA Martinez, Ulises Fair Division of Divisible Objects—Analysis of Allocation Methods with the Budget Constraint
2004 MAA Robbins, Tabitha Group Rational/Group Monotonic Allocation Methods on Four
Player Convex Games
2005 Goshen Huang, Jiayun (Aeron) Graphical Approach and Property Tests in Fair Division Problems with Indivisible Objects and Monetary Compensation
2005 Goshen Histand, Andrew The Range Nucleolus for Cooperative Games
2005 MAA Adenegan, Elizabeth Fair Division with Budget Constraints
2005 MAA Medrano, Jesus Partially Defined Cooperative Game Theory--A New Allocation Method
2005 MAA Mendez, Juan Embedded Coalitions Related to the Bell Triangle and Stirling Numbers of the Second Kind
2005 MAA Omer, Nada The Minimum Number of Efficient Allocations of Indivisible Objects
2005 Maple Tadjer, Rozalia Values for Partition Function Form Games
2007 Maple Shirk-Byler, Jesse Strategic Aspects of Fair Division
2008 Maple Richard, Gina Monotonic Power Indices
2008 Maple Yoder, Jason

The Evolution of Coalition Game Strategies

2009 Maple Unruh, Seth Envy-Free Divisions, Rose-Hulman Undergraduate Math Journal, Vol. 10, Issue 2, 2009
2010 MAA350 Helmuth, Erin The Notebook: A Mathematical Analysis
2010 MAA350 Hodges, Chaim Graph Coloring Games
2010 MAA350 Kooker, Patricia Modeling Shakespeare’s Romeo and Juliet as a Sequential, Strategic Game
2010 MAA350 Rody, Sarah Othello
2010 MAA350 Savage, Jonathan Evolutionary Game Theory and Economic Applications
2010 MAA350 Shelly, Aaron An Analysis of John Q
2010 MAA350 Weins, Ruth Fair Division of Household Chores (Excel data)
2011 Maple Hodges, Chaim Envy-Free Allocations for Two-Player Single-Good Allocation Problems with Money and Budget Constraints
2012 Maple Bontrager, Philip Fair Allocation Visualizations, Two-Person Inheritance Mathematica, Three-Person Inheritance Mathematica
2013 Maple Clemens, Andy n-Move Memory Evolutionarily Stable Strategies for the Iterated Prisoner's Dilemma
2013 Maple Schrock, Peter The Machiavelli Voting Power Index
2014 MA413 Ahlgrim, Garrett The Princess and the Roses
2014 MA413 Bontrager, Philip Traveling Purchaser Problem: A Greedy Approach
2014 MA413 Fretz, Emily Adding Death to the Fibonacci Sequence
2014 MA413 Shetler, Jacob A Specialized Case of the Euclidean 3-Dimensional Steiner Tree Problem
2014 Maple Ahlgrim, Garrett Expandable Stable Coexistence of Strategies
2014 Maple Pepala, Joel

U.S. Supreme Court Voting Power

2015 Maple Bitikofer, Kenan A Categorization of the Evolution of Spatial Cellular Automata in Symmetric Binary Decision Games
2016 MA413 Schrock, Peter The Flaw in the Machiavelli Index
2016 Maple Chen, Matthew Nucleolus and Group Monotonicity
2016 Maple Kaasa, Jon Allocation of Seats and Voting Power in the Norwegian Parliament
2017 Maple Bechler, Christian
Bitikofer, Kenan

A Counterexample to the Core Protocol of Aziz and Mackenzie

2018 MA413 Miller, Lydia Finding and Characterizing Knights Tours on the 4 x 4 x 4 Chessboard
2018 Maple Schrock, Nick Measuring Voting Power Using Observed Data
2019 MA413 Miller, Rae Ann Modified Collatz Conjecture
2019 Maple Abdelaziz, Ebtihal The Nucleolus for Partially De ned Cooperative Games
2020 Maple Abdelaziz, Ebtihal A Coalition Game on Finite Groups
2020 Maple Baer, Katie Quota Violations in the Apportionment Method of Webster


Allegheny Allegheny College senior thesis.
DREU National Science Foundation Research Experiences for Undergraduates summer program held at Drew University.
Goshen Goshen College honors thesis.
IQP Worcester Polytechnic Institute Interactive Qualifying Project.
MAA Goshen College Maple Scholars summer program. Support was obtained through the Mathematical Association of America's Strengthening Underrepresented Minority Mathematics Achievement Program, funded by the National Security Agency and the National Science Foundation.
MA300 Term paper for Math 300 Conjecture and Proof, the transition to advanced mathematics course at Goshen College until 2003.
MA350 Term paper for Math 350 Game Theory course at Goshen College.
MA413 Paper for Math 413 Discoveries Seminar 1-credit course at Goshen College.
Maple Goshen College Maple Scholars summer program.
MQP Worcester Polytechnic Institute Major Qualifying Project.
Rutgers Rutgers University senior thesis.
WREU National Science Foundation Research Experiences for Undergraduates summer program held at Worcester Polytechnic Institute.