How much impact can a set of free game theory infographics have?

A few years ago, I worked with graphic designer Greg Riestenberg to come up with a series of infographic images designed to make several foundational game theory constructs easier to understand. Our approach was to take all the numbers out of the representations, using information design to highlight how the games work and how they differ from each other. We then put the images up for free use via a Creative Commons BY-SA license.

So what happens when you make a series of graphics designed to solve a problem freely available on the web? Today I decided to anwer that question, so I searched on “Chris Jensen Greg Riestenberg” using Google in an attempt to find all of the instances where our images had been used.

Below is a summary of what I found, listed by image starting with the images that were most frequently incorporated into websites and attributed to us…

The Prisoner’s Dilemma, embezzlement matrix:

Towards the end of our project, Greg decided that he wanted to create a set of images that communicated the archetypal story of the prisoner’s dilemma. He settled on an embezzlement scheme where two corrupt businessmen conspired to steal money and use it to fund a lavish retirement… as long as neither ratted out the other. The main component of this story was an interactive PDF that allowed users to play with the possibilities inherent in the prisoner’s dilemma, but Greg also made a matrix version of this story. This has turned out to be the most widely-used images of those that I could discover. I can’t fully account for the popularity of this image: perhaps it’s favored because it tells the literal story of prisoners, but it also has the richest graphic imagery of any of the images we created. You can find this image used on these sites:

Mashable “Why mathematician John Nash was a genius“

Master Informatique, Spécialité ANDROIDE “Algorithms for Optimization and Game Theory“

Sinnerman “A beautiful mind passed away“

Elle Turner “Let’s do the irrational thing“

The Prisoner’s Dilemma, military metaphor:

This was one of the earliest “example” matrices that Greg created. The idea was to show how the logic of a real-world situation could be applied to matrix logic of the prisoner’s dilemma. This is the “cold war” scenario, wherein two countries must decide whether to cooperate by saving their resources for peaceful purposes or defect by using their resources to build an atomic bomb. I am not surprised that this matrix has been used frequently, because the cold war standoff is one of the most frequently-invoked “real world examples” of a scenario that might resemble the prisoner’s dilemma. The cold war itself — and the waste that failure to cooperate created — are also culturally-prevalent ideas. You can find this image used on these sites:

HubPages “Mark Lynas’s “Six Degrees”: A Summary Review“

Tetragonal Lattice “Game theory research tells you, “it” is the master of the world”
(title as translated by Google Translate, which might be really off)

Talaios “Competitiveness and cooperation“

The Stag Hunt, stags and rabbits metaphor:

While the prisoner’s dilemma is the most commonly-explored evolutionary game construct, there are also two other versions of these two player games that also encapsulate a social dilemma: the stag hunt and hawk-dove games. The stag hunt, originally conceived of by Rousseau, envisions a cooperative dilemma that was probably faced by our ancestors: to hunt together for big game or to hunt separately for small game. Greg created this nice, extremely simple “example matrix” that shows the payoff to two hunters who each choose to either cooperate to collaboratively hunt big game or defect by seeking their own small game. You can find this image used on these sites:

Principia Naturaliss “Rousseau and………math?“

Thinking is the best way to travel “Infographics abound“

The Prisoner’s Dilemma, black-and-white “briefcase” example matrix:

Most of the two-player games that we chose to depict involve simultaneous strategy choices by each player. This might be one of the most unrealistic aspects of these game constructs, because in the real world you need to dig pretty deep in order to find a scenario where socially-interacting individuals actually make blind choices about how the behave in relation to each other. One such scenario would be an exchange of sealed briefcases: if each individual assumes that there is potential for a mutually-beneficial exchange of cash-for-goods, then the dilemma is whether or not to actually cooperate by providing a briefcase that’s not empty. Here we create an image that evokes some sort back-alley exchange of cash for (potentially stolen) goods. You can find this image used on these sites:

Integrated Carbon Observation System “Director’s Corner: Cooperation in a Competitive World“

Contemplating Cognition “A downside to the ‘love drug’“

The Prisoner’s Dilemma, sequence of play infographic:

I have found that a lot of students struggle to understand the actual sequence of events represented by these two-player games, so Greg and I endeavored to show the full dynamics of each game with a simple “sequence” image. What I really like about these images is that they tell you pretty much everything that you need to know about these games. Greg created a very simple graphic convention for all the games, which allowed us to create images that make for easy comparison of the similarities and differences between different game conventions. If there was one image type that I wish was being used more prevalently, it would be these sequence images. You can find this image used on these sites:

Hashing It “Prisoner’s Dilemmas?“

Master Informatique, Spécialité ANDROIDE “Decision and Games“

The Prisoner’s Dilemma, conceptual representation with numbers:

One of our stated goals with this project was to make numbers an unnecessary part of understanding these games. As such, you could argue that we caved a bit by producing an image that was basically a colorized version of a numerical matrix. Our original idea was that this image could be used after the non-numerical conceptual images to bridge students from the conceptual to the numerical. Nonetheless, this image is being used by itself rather than as part of the package of images it originally belonged to. You can find this image used on these sites:

The Scientist “A Twist in Evolutionary Game Theory“

Chris Harland “Chicago Bars, Prisoner’s Dilemma, and Practical Models in Search“

Other images used:

The rest of the images that I discovered in use all were used just once. Perhaps the most prominent use of one of our images appeared in a blog post on U.S. negotiations with Iran featured on the website of The Atlantic Monthly; the image used was one of our sequence images depicting the ultimatum game. Shared over 1000 times on Facebook, I have to guess this post is responsible for the most views of our images. There’s also a use of the sequence image depicting the hawk dove game on a LinkedIn post.

Perhaps the most striking reality is that none of our “conceptual representations” (such as this one) have been used on the web. But an image meant to complement these conceptual representations has been used, as has the numerical representation discussed above.

And although it is a bit more difficult to track the use of a PDF, a couple of sites (here and here) have used Greg’s interactive PDF depicting the embezzlement version of the prisoner’s dilemma.

Awesome, disappointing, or neither?

This is an unscientific survey of the use of these images, so it is perhaps a bit risky to try to draw too many conclusions from what I have discovered. Considering all the work that we — and especially Greg — put into making these images, perhaps I should be bummed out that only the handful of sites listed above have made use of the images. Of course I wish that there had been too many uses to bother chronicling.

But I think that there are several reasons to be heartened by the use of these images thus far. The first is that these are just the images that were properly attributed and used on the open internet. We have no idea how many other times these images were used and not attributed, or were used in some format (a book, a presentation) that is not searchable on the web. I tend to imagine — perhaps without a lot of basis — that for every “findable” use of these images there must be many more “unfindable” uses.

The other reason for optimism is that many of these images have been used in fairly prominent places, which means that people have seen them. And a few are clearly being used in educational settings, a great use given the original goals of the project. The images could be used in countless other educational settings without us ever knowing, as most curriculum is not online or at least hidden behind access walls of learning management systems.

If there’s anything profound that I am taking away from this little survey, it is that one aspect of our project appears to have been pretty unsuccessful: the conceptual images that were the foundation of our project just don’t seem to be in use. Perhaps not surprisingly, the “example” matrices are far more “popular”: perhaps the gap that needed to be filled conceptually was not so much for matrices that lacked numbers but for matrices that contained ideas. The ideas in our example matrices seem to be more valuable to our users (although I am still very disappointed that no one has used the bubble-feeding whale example matrix, which is my favorite).

And the surprise winner seems to be our “sequence” images, which were conceived of later in the project. If my memory serves me correctly, these were entirely Greg’s inspiration, and they were very smart: these images capture all the basic things you need to know about these games in a single image. In this sense the sequence images are far superior to the matrices, so I am not surprised to see them used, albeit sparingly. Perhaps making our original conceptual matrices was a necessary step towards the eventual creation of these sequence images. Sometimes what seems like a creative failure is just a step towards creative success.

I am tremendously proud of having worked with Greg on these images. It’s only three years out since their release, and it will be interesting to see if their use accelerates or fades away in future years. Either way, we have created something that people use, and to me that’s a valuable outcome of the project.

Looking for all the images in this project? You can find them either here or here.