Professor of Mathematics and Statistics

Loyola University Chicago

Office Hours for Sp 2019:  TTh 11:30-1:00 or by appointment. 

Department of Mathematics and Statistics
607 BVM
phone:  (773) 508-3575
If you want to send me an email message click on the address below:




Go Directly to Sakai


Classes for Sp 2019


1.        Math/Stat 304 Probability (see the Course Description at Course Offerings

2.        Math 132 Intro to Calculus II (see the course description at Course Offerings.




A talk delivered in the Undergraduate Colloquium series was an introduction to problems covered in game theory. The slides for the talk are available here :Introduction to Game Theory






These classes are accessed through http://www.sakai.luc.edu/. You get on to Sakai using your Loyola userid and Password.








Text: Game Theory, An Introduction, Second Edition, by E.N.Barron, published by John Wiley & Sons, Inc., 2013. Buy from AMAZON.COM, or Half.com.


Errors for Edition 2 will be available by clicking here Errata for Second Edition


Errors for Solution Manual to Accompany Game Theory: An Introduction, published by John Wiley & Sons, Inc., 2013, is available by clicking Errata for Solution Manual


All errors for Edition 1 will be available by clicking here Game Theory, An Introduction: Errata



The book (Edition 1)is currently in the 3rd printing.


The following Maple and Mathematica worksheets were written to be used with the book. They are offered here with absolutely no warranty.

Maple worksheets for the class:Chaps 1 & 2

Chap 3

Chap 4

Chap 5

Chap 6

Mathematica Notebooks


New Mathematica Notebooks

Linear Programming Solution Zero Sum Games

Graphical Solution for 2Xm or nX2 Games

Lemke-Howson Nash equilibria

Nucleolus and Shapley for Cooperative Games

Exact Solution 3 player Cooperative Game

Exact Nucleolus Nonempty Core Cooperative Game


I have written a procedure to find the Shapley Value for any N-person Cooperative game given the characteristic function. In addition it gives a systematic way to find the Nucleolus of the game. You may download this worksheet by clicking on Shapley-Nucleolus.


Some of the Mathematica Notebooks may need to be updated to the latest version of Mathematica.


All of the figures in the book which were created with Maple can be downloaded by clicking on Figures.




Important game solving links:

1. Gambit This is a program which will solve any N-player nonzero sum game. As a particular case, it can solve any zero sum 2 person game by entering the payoffs as a_ij for Player I and a_ij for Player II. It is available directly from http://www.gambit-project.org, by McKelvey, Richard D., McLennan, Andrew M., and Turocy, Theodore L. (2010). Gambit: Software Tools for Game Theory, Version 0.2010.09.01.

2. Game Theory Website

3. The Mathematica package that can solve any characteristic function cooperative game was written by Professor Holger Meinhardt and is available from

http://library.wolfram.com/infocenter/MathSource/5709/. The newest version is available by clicking here.


If you are using MatLab, Professor Meinhardt has a package available which can do the same thing available at



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Dr. Barron received his PhD in 1974 in Mathematics from Northwestern University specializing in Partial Differential Equations and Differential Games. In 1972 he received an M.S. degree in Applied Mathematics from Northwestern University, and in 1970 he received a B.S. degree in Mathematics from the University of Illinois at Chicago. His research interests include partial differential equations, calculus of variations, optimal control and differential game theory, stochastic processes, probability theory, mathematical finance, and game theory. He has been the recipient of numerous National Science Foundation grants, Air Force Office of Scientific Research Grants, and has been named a Master Teacher in the College of Arts and Sciences.