Can ChatGPT Solve Coordination Games? Game Theory Meets AI in the Classroom

Can AI Solve Game Theory Problems?

Large language models (LLMs) like ChatGPT are changing how we complete tasks and approach problems. But how well can they handle game theory problems—especially those that require logic, not just math?

This semester I’m teaching game theory, and as part of the course, I plan to explore how students can use and learn from AI. To start, I wanted to see how well ChatGPT could solve a particular type of problem that relies on strategic thinking and logical prediction: the coordination game.

What is The Coordination Game?

A coordination game is one in which players benefit from aligning their choices with others. Because of this, there are often multiple possible Nash equilibria—stable outcomes where no player has an incentive to unilaterally change their choice.

This concept has real-world applications, especially in business. Companies often try to anticipate consumer behavior and align their strategies accordingly.

In my game theory course, I introduce students to the coordination game with a fun, simplified classroom exercise. I ask the class a question. Each student who gives the most common answer—not the “correct” one, but the one most others give—wins a small prize.

For example, if I ask “What color is the sky?” and everyone says “blue,” everyone wins. If 51% say “blue” and 49% say “red,” the blue group wins. But if 51% say “red,” they win—even though red isn’t factually correct. The key is predicting what others will say.

What is a Coordination Game Question I Ask my Students?

There is one coordination game question I used to always ask my students. (Note, since I’m posting this publicly and some of my students will read this, I’ll have to come up with others.) That question is:

What is the fifth most populous city in the United States?

Note - before reading further, take a moment to think about how you would answer this if you were in my class. Remember, you want your answer to be the most commonly answer given.

What was your guess? Well, you could search and easily find that the fifth most populous city in the US is Phoenix. But that doesn’t really matter. What matters if you match the most common answer given by the class.

I’ve run this game this many times in my class and every single time the answer has been Philadelphia. Why? Students generally know Philadelphia isn’t the first or second biggest city. They also know it is a big city and at only 2.5 hours from our campus is the closest. There are even students in the class who are certain this Philadelphia is not really the fifth biggest city, but put down Philadelphia to win.

That raises a question of how would ChatGPT answer? Before asking the question, I wasn’t sure. This isn’t like a problem with a calculator, after all. So what happened?

Did ChatGPT Solve the Coordination Game?

I wrote into ChatGPT:

Do you know what the coordination game is? It is a game where someone answers a question and they "win" if their response is the most commonly given answer from the group. Under these rules, I teach at a University in Pennsylvania. If I asked what the 5th most populous city in the US is, what would you answer?

ChatGPT said:
Yes, that’s a classic example of a coordination game—where players benefit from matching the answers of others rather than being factually correct. The goal is to anticipate what others think is the common answer, not necessarily the right answer.

If I’m playing this game with college students in Pennsylvania, and I’m aiming for what’s likely to be the 5th most commonly guessed U.S. city by population (not necessarily the actual 5th largest), here’s the reasoning:

Most people can easily name:
New York
Los Angeles
Chicago
Houston

Those are usually top of mind. The 5th spot becomes trickier.
The correct answer by actual population is Phoenix, Arizona.

But in a coordination game, Philadelphia might be a more common guess—especially in Pennsylvania—because:
It’s very well-known locally.
It was once among the top 5.
Students may not update for recent growth in Sun Belt cities.
So my coordination game answer is: Philadelphia.

I was floored at the response. If this isn’t perfect reasoning, it’s really close. As someone who is teaching this fall, it has me questioning what is most valuable to teach and how should I teach it.

So I figured I’d try another one.

A Second Coordination Game Problem

Another coordination game question that I would often give my students is “What is the capital of the state of Washington?"

What answer would you give in the coordination game? ChatGPT gives good rationale and a response that would consistently win if playing in my classroom. (See below the graphic.)

ChatGPT answered:

In a coordination game, while the correct answer is Olympia, most people—especially those less familiar with U.S. geography—might instinctively guess Seattle, because:
It’s by far the most well-known city in Washington.
Many assume the largest city is the capital.
It's often mistakenly identified as the capital in casual conversation.
So for a coordination game, my answer would be: Seattle.

What does this mean? I’m not entirely sure yet—but it’s certainly worth reflecting on.

If ChatGPT can reason this well about human behavior, even in informal settings like a coordination game, it raises questions about how we should teach strategic thinking and decision-making.

I’ll be posting more about game theory throughout the semester as I explore how to integrate AI tools into the classroom. And there likely will be more game theory and pop culture posts as well. So stay tuned!