Which Game Are We Playing?

Imagine you're at the beach and want to buy an ice cream. Several vendors sell the same ice cream at the same price.

You will probably choose the one closest to you.

Now imagine you're the vendor. Where should you set up your stand?

The answer seems simple: somewhere close to where the customers are.

But what if two other vendors arrive?

Now your location depends not only on where the customers are, but also on where the other vendors decide to go.

Suppose you repeat this every day, and whoever arrives first can choose any available spot.

Where would you position yourself?

Would you try to be close to the largest number of customers? Would you avoid the other vendors? Or would you try to anticipate where they might go?

And does being the first to choose necessarily help?

This is roughly the idea behind the Lemonade Stand Game, a problem from multiagent systems research. In the original game, three players choose locations around a circular beach, without communicating, and repeat the game over many rounds.

Try the circular-beach experiment →

The Other Vendors Are Thinking Too

You could choose your location based on where the other vendors were yesterday. But what if they're doing the same thing?

You might try to anticipate their moves. And perhaps they're anticipating yours.

How many steps ahead should you think?

This connects to levels of reasoning in game theory. But more reasoning isn't necessarily better. You certainly can overthink your strategy.

Because the game repeats, you can also learn from what happens and adjust your strategy.

So perhaps the question is not only what the best location is, but how much you actually know about the other players.

Outside the Game

One useful characteristic of the Lemonade Stand Game is that everyone has the same objective: attract as many customers as possible.

You don't know what the other players will do, but at least you know what they're trying to achieve.

In real situations, we often don't even know that.

Consider a job interview. You might prepare to demonstrate your technical skills, while the interviewer is more interested in how you work with other people.

You might give excellent answers and still fail to address what the interviewer really wanted to know.

Something similar can happen in negotiations or collaborations. We make assumptions about what other people want and then try to anticipate their decisions.

But there is a difference between predicting what someone will do and understanding what they're trying to achieve.

In the Lemonade Stand Game, we know what everyone wants. We need to figure out how they'll play.

Outside the game, we might spend a lot of time developing a good strategy based on what we assume the other person wants.

But what if that assumption is wrong?

We might be playing perfectly, just not the same game.