[WSG76] Daily Study Group: Introduction to Game Theory

Ideas
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A Wolfram U Daily Study Group on game theory begins on Monday, March 30, 2026.

Join me and a group of fellow learners to learn about the basics of game theory. Our topics for the Study Group include:

  1. Simultaneous games
  2. Sequential games
  3. Repeated games

Make the right decision and learn the art of making decisions mathematically and rationally!

No prior Wolfram Language experience is required.

Please feel free to use this thread to collaborate and share ideas, materials and links to other resources with fellow learners!

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March 30–April 3, 11am–noon CT (4–5pm GMT)

REGISTER HERE

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Feel free to share this post on social media using the hashtags #WolframU and #DailyStudyGroup.

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In this delightful course, Marc Vicuna has skillfully blended a discussion of the computational tools for game theory in the Wolfram Language with an examination of the fundamental ideas of modern game theory.

I strongly recommend this short, one-week Study Group to everyone!

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Question on exercise 2 - cheating students.
Proposed solution has these payoffs:

payoffs = {{{{0, 0, 0}, {0, 0, 1}}, {{0, 1, 0}, {0, -1, -1}}}, {{{1, 
      0, 0}, {-1, 0, -1}}, {{-1, -1, 0}, {-1, -1, -1}}}};

However, since this is a zero-sum, they need to be normalized. Is there any benefit to doing so vs defining payoffs as zero-sum integers like below?

payoffs = {{{{0, 0, 0}, {-1, -1, 2}}, {{-1, 
      2, -1}, {2, -1, -1}}}, {{{2, -1, -1}, {-1, 2, -1}}, {{-1, -1, 
      2}, {0, 0, 0}}}};
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Hi;

Why am I not getting the actions listed in my MatrixGamePlot function - see attached notebook?

Thanks,

Mitch Sandlin

ThePrisonersDelimma.nb (51.3 KB)

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I can see the actions with game["Dataset"]:

Custom-Prisoner-Dilemma-actions.png
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Using “Dataset” displays the actions, but it is missing the players legend. What I am looking for is one graphic that shows all necessary information. If you are using the graphic to determine what action to take, you need the: players, actions, and payoffs to make the decision and shouldn’t need to mentally combine several graphics to get the information.

Thanks,

Mitch Sandlin

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Hi Mitchell,

As explained in the class, this was a design decision, as both representations emphasize different aspects of matrix games. However, to alleviate this issue, tooltips reveal both players and actions on both representations.
Worst case, if you need matrix games as a PNG, you could always legend the dataset fairly quickly, keeping in mind it would cease to be a Dataset.

Best,
Marc Vicuna

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I missed the study group session 4 due to I had another duty am I please still qualifying for the certificate ?

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Hi;

How would you set-up a matrix for the Rock,Paper,Scissors game?

Thanks,

Mitch Sandlin

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RockPaperScissors is a zero-sum simultaneous game. There are 3 outcomes: {1,-1} (the first player wins and the second loses), {0,0} (a tie) and {-1,1} (the first player loses, the second wins). Then, its a question of forming the matrix game. Consider the second player plays in order, rock, paper and scissors, consider the outcomes if player 1 chooses rock: {{0, 0}, {-1, 1}, {1, -1}}, paper: {{1, -1}, {0, 0}, {-1, 1}} and scissors: {{-1, 1}, {1, -1}, {0, 0}}. So your payoff array is {{{0, 0}, {-1, 1}, {1, -1}}, {{1, -1}, {0, 0}, {-1, 1}}, {{-1, 1}, {1, -1}, {0, 0}}}. Then, I would set up the GameActionLabels at {{“Rock”,“Paper”,“Scissors”},{“Rock”,“Paper”,“Scissors”}}, and the GamePlayerLabels, if we were to play together for example, as {“Mitchell”,“Marc”}.

So in total the call would be

MatrixGame[{{{0, 0}, {-1, 1}, {1, -1}}, {{1, -1}, {0, 0}, {-1, 1}}, {{-1, 1}, {1, -1}, {0, 0}}},
GameActionLabels -> {{"Rock", "Paper", "Scissors"}, {"Rock", "Paper", "Scissors"}}, 
GamePlayerLabels -> {"Mitchell", "Marc"}]

Best,
Marc Vicuna

1 Like
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Hi Michael!

This was answered in class. Overall, zero-sum games have a few simple theorems, like the Minimax Theorem, the Equivalence of Nash Equilibria and Minimax Strategies, the Interchangeability of Equilibria, the Linear Programming Duality Formulation, the Saddle Point Characterization, the Zero Duality Gap (Strong Duality Interpretation), etc. that make them very easy to analyze mathematically. However, another thing to keep in mind is that some games can be transformed into zero-sum games as long as the ordering of payoffs is maintained. As long as the ordering is the same, the number of equilibria is also the same.

Best,

Marc Vicuna

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I did not receive the email yesterday or today with the session recording. Are they available somewhere?

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Hi, Mark! I forwarded the recordings to your email address, along with the additional information we shared during those sessions. You can also access them by clicking this link, which takes you to the series’ landing page. Thank you for your participation in this Study Group!

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The Wolfram U framework for this course will soon be available! Thank you for your patience.

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Hello Georgios Tsolakis,

As mentioned in the study group, the certification is based on passing the quizzes and final exam. Thus, when the course is available on Wolfram U, you’ll be able to get your certification.

Best,

Marc Vicuna

1 Like
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Hi Marc;

This matrix works great; however, it looks like a vector if you view it in //MatrixForm, which was unexpected. Additionally, if you enclose each number of the matrix in another set of {} and view it using //MatrixForm, it looks the same. The matrix for the game works fine, I just didn’t expect it to look like a vector and cannot understand why it looks like a vector.

Thanks,

Mitch Sandlin

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Good day!
I understand that the framework for the course will be available soon, but I’d like to ask if this will be before 14 April 2026. This is because my Wolfram Mathematica student trial will be expiring by then.
Thank you so much! :slight_smile:

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Hello. After the last class on game theory, all the participants have received an email for the recording. That email said “We will share a link to the Introduction to Game Theory framework, including access to the quizzes and final exam, in an email when the new interactive course is released.”

I believe that we have not received this link yet. Will we receive the link soon? Also, if we want to solve the quizzes and pass the final exam, will we have enough time to do them?

Thank you.

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I’m happy to announce that the new course has been released and is freely available in the Wolfram U catalog: Introduction to Game Theory

Thanks to everyone for their contributions during this development cycle. Sign in using your Wolfram ID (or create one to get started), and receive access to all the video lessons, quizzes, a sample exam, the final exam and certifications. The interactive course includes a progress tracker where you can monitor your progress toward a completion certificate. Take the final exam to earn a Level 1 certification for proficiency in game theory. Enjoy!

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Using PlotLegends, I cannot seem to specify the text for the legend in the evolutionaryDynamicalSystemPlot function for the HawkDove Game in the last lesson.

Does the Legend need to be included in the formalization of the general function evolutionaryDynamicalSystemPlot before it can be formatted in the plot of a specific evolutionary game (example)?

If so, what is the appropriate Wolfram Language for that?

Thank you,

Steve Anderson