Dynamo: Diagrams for Evolutionary Game Dynamics

by Bill Sandholm, Emin Dokumaci, and Francisco Franchetti

Introduction

Dynamo is a suite of easy-to-use Mathematica notebooks for generating phase diagrams, vector fields, and other graphics related to evolutionary game dynamics.

The four phase diagrams above were generated using the four Dynamo workbooks. (In the first two figures, colors reflect speed of motion: blue is slowest, red is fastest.)

• Top left: The logit(.28) dynamic in a three-strategy pure coordination game.
• Bottom left: The Smith dynamic in Rock-Paper-Scissors-Twin.
• Top right: The best response dynamic in Matching Pennies.
• Bottom right: The replicator dynamic in Mismatching Pennies.

For more pictures and animations, visit the project gallery.

Download the Dynamo v.1.1 workbook here:

• Dynamo 3S. For one-population, three strategy games (posted 30 August 2011).

Download the Dynamo v.0.2.5 workbooks here:

• Dynamo 4S. For one-population, four strategy games (posted 9 May 2010).
• Dynamo 2x2. For two-population, 2 x 2 strategy games (posted 9 May 2010).
• Dynamo 2x2x2. For three-population, 2 x 2 x 2 strategy games (posted 9 May 2010).

Dynamo v1.1 and v0.2.5 run in Mathematica 6, 7, and 8. They do not run in Mathematica 4 or 5. For the legacy version (0.1.5) that does, visit here.

Working with Dynamo

Dynamo is free, open source software.

If you use Dynamo in your work (e.g., to create figures for articles or books), we would be grateful for your citation.

W. H. Sandholm, E. Dokumaci, and F. Franchetti (2011). Dynamo: Diagrams for Evolutionary Game Dynamics, version 1.1. http://www.ssc.wisc.edu/~whs/dynamo.

Dynamo in print

I am maintaing a list of papers and books containing figures created in Dynamo - and here it is.

Please e-mail me with any feedback you have about the program, or to have your publication added to our list.

Project history

In 2003, I began working on Dynamo when I realized I would need to create many illustrations of game dynamics for my book on evolutionary game theory. Emin Dokumaci was the lead programmer of Dynamo from 2003-2007, and did most of the coding of the Mathematica 4/5 version of the software.

In 2007, Wolfram released Mathematica 6, which included some impressive new features (like rotatable 3D graphics), but also many small changes in the programming language that made code written for older versions of Mathematica behave badly. Grrrr. So the code was frozen, until...

In 2010, Francisco Franchetti became the new lead programmer of Dynamo, and he gamely updated the Dynamo code to run Mathematica 6/7.

In April 2011, Francisco and I completed a polished version of Dynamo 3S, which we have (after only eight years!) dubbed version 1.0. The corresponding updates of the other notebooks are underway.

Other free game theory software

The Gambit library, by Richard McKelvey, Andy McLennan, and Ted Turocy, provides a variety of tools for drawing and (especially) solving normal and extensive form games.

Christoph Hauert's VirtualLabs in evolutionary game theory provides tools for studying evolutionary dynamics in spatial games - that is, games played by agents located at points on lattices or other graphs. The animations are amazing - see for yourself!

Acknowledgement

I am grateful for financial support from the National Science Foundation under Grants SES-0092145, SES-0617753, and SES-0851580.

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