Dynamo

Introduction

Dynamo is a suite of easy-to-use computer programs for generating phase diagrams, vector fields, and other graphics related to evolutionary dynamics from game theory. Emin Dokumaci and I have been working on Dynamo since January of 2003. The programs are Mathematica notebooks; they are written for Mathematica 5.x, but most features work in Mathematica 4.1 as well.

The four phase diagrams above were generated using the four Dynamo programs. (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.
• Top right: The best response dynamic in Matching Pennies.
• Bottom left: The pairwise difference dynamic in Rock-Paper-Scissors-Twin.
• Bottom right: The replicator dynamic in Mismatching Pennies.

Animations

While the pictures above are unedited Dynamo output, one can combine multiple output files to create animations. For example, take a look at

• Chaos in Rock-Paper-Scissors. Follows the progress of a single unpredictable solution trajectory.
• Logit dynamics in 123 Coordination. Illustrates how the phase diagram of the logit dynamic changes as one varies the noise level.

Downloads

For more information about Dynamo, take a look at some annotated screen shots that Emin has posted here. Or try Dynamo for yourself: click on one of the links below, save the page that appears into a new file, and open the file in Mathematica.

• Dynamo 3. For single-population, three strategy games (version 1.4.2, 4/11/07).
• Dynamo 2x2. For two-population, 2 x 2 strategy games (version 1.1.1, 4/11/07).
• Dynamo 4. For single-population, four strategy games (version 1.1, 7/31/06).
• Dynamo 2x2x2. For three-population, 2 x 2 x 2 strategy games (version 1.1, 7/31/06).

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 and E. Dokumaci (2007). Dynamo: Phase Diagrams for Evolutionary Dynamics. Software suite. http://www.ssc.wisc.edu/~whs/dynamo.

Other free game theory software

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

Feedback

Please e-mail me with any feedback you have about the program.

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