Where would you put your stand?
This is a small experiment in making a choice when other people can choose too. Move the stands and watch how many customers each one serves. Then see how the same stand positions perform when customers are concentrated along one stretch of the beach. Finally, make a move before seeing what the other vendors do.
There are three views to try:
- Evenly spread: Move the stands and see how their positions affect customer share.
- Crowded stretch: Keep those positions, but change where the customers are.
- Next day: Choose your position, predict the result, and reveal the other vendors’ moves.
Three vendors sell the same ice cream at the same price. Each wants as many customers as possible. Each customer chooses the nearest stand along the circular shore.
Inspired by the Lemonade Stand Game: lemonade in the original, ice cream here. This is a simplified adaptation; the first two views allow free movement, while the third uses twelve locations and repeated rounds.
Drag a stand around the shore, or use the sliders. The other stands stay where you leave them.
The shaded arc is the crowded quarter. Its three rows of dots show the higher density. Stand positions stay the same when you switch views.
Choose A’s next location by dragging or using its slider. The twelve pale dots are available spots.
View 1 · Evenly spread
The 100 customers are equally spaced around the shore. Try moving one stand while leaving the others in place: a better position for one vendor can mean fewer customers for another. The other stands do not move on their own in this view.
View 2 · Crowded stretch
Sixty customers now occupy one quarter of the shore, while forty occupy the rest. The stands keep their positions when you switch between the first two views, so you can see how the same locations perform when demand changes. This crowd is an illustrative scenario, not a real-beach estimate.
View 3 · Next day
Customers are evenly spread again. Choose A’s spot and compare your prediction with the result after B and C move. They each use a simple rule based on yesterday’s positions; real competitors need not follow it.
Customer share
Each customer goes to the nearest stand along the shore. If two stands are equally close, they split that customer.
Same stand positions; only the customer distribution changed.
Place A for tomorrow. B and C are still shown at their previous positions.
What changed?
Randomize moves all three stands; the customers stay in place.
If B and C stay where they are, A would serve — of customers.
Choose a prediction to reveal the next day. “Not sure” is fine.
How do B and C choose?
Each independently picks the spot that would have served them best if yesterday’s other stands stayed put. They cannot see your new choice or each other’s new choice. If spots tie, they prefer the one closest to yesterday’s spot.
Days played
What the experiment leaves us with
A good location depends on where customers are and where the other vendors choose to stand. Changing either can change the result. In the third view, even a careful estimate based on today’s positions can be wrong when the others move tomorrow.
Here, we know the rules: every vendor wants more customers, and customers choose the closest stand along the shore. Outside a small model, we may not know what the other person is trying to achieve in the first place. That is the question behind “Which Game Are We Playing?” →