TUGlab  TUGlabExtended
Transferable utility game theory Matlab toolboxes
Authors
We wish to acknowledge the support of the Santiago Game Theory Group.
TUGlab information
The toolbox TUGlab (Transferable Utility Games laboratory) is a Matlab set of scripts that could serve as a helpful complement to the books and other materials used in introductory courses on cooperative game theory. Its main goal is to emphasize the geometrical aspects of cooperative game theory. TUGlab offers to both the instructor and the student a tool to compute and visualize basic concepts for any given 3 or 4 persons TU game. It allows the user to experiment at will with games without worrying about the mathematical complexity of the computations. That is the power of this platform: its direct and flexible way of going to the heart of the concepts overcoming the mathematical complexity.
The TUGlab platform works on any implementation of the later releases of the Matlab product: Matlab 6 and Matlab 7 on Unix, PC or Macintosh. It is a collection of 58 files including:
To install it, just copy and paste the folder TUGlab on your hard disk. Then,
include this directory in the Matlab search path. All the TUGlab functions can
be run directly from the Matlab Command Window. The characteristic function
of the game must be introduced as a vector
A=[v(1) v(2) v(3) v(12) v(13) v(23) v(123)], for 3persons games, or
A=[v(1) v(2) v(3) v(4) v(12) v(13) v(14) v(23) v(24) v(34) v(123) v(124) v(134) v(234) v(1234)], for 4persons games.
We include some illustrative examples on how to use the toolbox. These are:
TUGlabExtended information
The toolbox TUGlabExtended is a Matlab set of scripts that extends the TUGlab package, that only works for 3 and 4 person games, to cover an arbitrary number of players. Therefore, it does not include graphical features.
The TUGlabExtended platform works on any implementation of the later releases of the Matlab product: Matlab 6 and Matlab 7 on Unix, PC or Macintosh. It is a collection of 24 files including:
To install it, just copy and paste the folder TUGlabExtended on your hard disk. Then, include this directory in the Matlab search path. All the TUGlab functions can be run directly from the Matlab Command Window.
The characteristic function of a nperson game must be introduced
as a 1x(2^n1) vector following the order induced by the binary representation
of the coalitions:
Position  Binary  Coalition 
1  100  {1} 
2  010  {2} 
3  110  {1,2} 
4  001  {3} 
5  101  {1,3} 
6  011  {2,3} 
7  111  {1,2,3} 
The table below shows how the execution time (in seconds) of some TUGlabExtended commands increases with the number of players.
Players  Shapley value  Tauvalue  Checking convexity 
3  0.016912  0.004057  0.000732 
4  0.050173  0.001219  0.000766 
5  0.141409  0.002493  0.002999 
6  0.385369  0.005456  0.012129 
7  1.012571  0.012438  0.049606 
8  2.579563  0.028435  0.201198 
9  6.418109  0.064519  0.801556 
10  15.546376  0.145796  3.294879 
11  37.162233  0.325364  13.314801 
12  87.538653  0.842787  52.558724 
13  203.704998  3.903356  209.971761 
14  471.142136  12.000016  837.683950 
15  1080.910514  37.075949  3419.695234 
Software and documentation  

Last revision: April, 2009.
Please, report bugs or comments to mmiras@uvigo.es or esanchez@uvigo.es.
Please, acknowledge the authors if you make use of TUGlab or TUGlabExtended in your teaching or research.