# The Lemonade Stand Game

 About Rules Code 2009 2010 2011 Forum The Future

## Introduction

Imagine the following game. It is summer on Lemonade Island, and you need to make some cash. You decide to set up a lemonade stand on the beach (which goes all around the island), as do two others. There are twelve places to set up around the island like the numbers on a clock. Your price is fixed, and all people go to the nearest lemonade stand.

The game is repeated. Every night, everyone moves under cover of darkness (simultaneously) and in the morning, their locations are fixed. There is no cost to move. After 100 days of summer, the game is over. The utility of the repeated game is the sum of the utilities of single-shot games.

## Rules of the Game

On every spot of the island, there are 6, 12, or 18 customers. Everyone goes to the nearest location, with ties split randomly. You get 1 dollar for each person that comes to your lemonade stand.

For example, suppose there are 12 customers at the 3 o'clock location. Alice sets up at 1 o'clock, and Bob and Candy set up at 5 o'clock. Then, 4 of the customers from 3 o'clock will go to Alice, 4 will go to Bob, and 4 will go to Charlie. If there are 6 customers at 2 o'clock, they will go to Alice. If there are 18 customers at 4 o'clock, 9 of them will go to Bob and 9 will go to Charlie. And so on, and so on.

Since the total utility of different games is different, the first game in each series will be the same, the second game in every series will be the same, et cetera. There will be 100 games in each series, if possible.

## New Rule This Year

In the past, each 100 iterations, we would reset every player. That would create statistical significance in the results. This year, players will be allowed to remember some history. This will give them the potential to learn the styles of their opponents and adapt to them.

## Simple, Yet Hard

"Listen, here's the thing, if you can't spot the sucker in your first half hour at the table, then you are the sucker." - Rounders

The game now has a bit of structure, but there is still no right action. In particular, if you sit on a spot with a utility of 18, you can still do very badly if the other two players flank you.

## How Older Algorithms Fare

What is also interesting is that playing on opposite sides of the circle no longer is fair and balanced, even if the third player is playing randomly. Again, a simple strategy that plays a constant strategy on the best half of the current game beats all the bots from the 2010 competition. So, this game incorporates a small amount of game complexity with a great deal of computational analysis.

## The Game is not Real, but the Players Are

One frustrating thing about poker research and auction research is that one can become so lost in the mechanism and the dynamics of the game, one forgets about the players inside the game. As researchers, we often focus on learning the game, then forget about the people playing it.

The effort behind this competition is to unask the question of how to play the game, and instead focus on how to play the players in the game. In effect, this game is as simple as rock paper scissors, in that symmetries between actions leave nothing to the imagination. What makes the game complex is the people who are playing it.

The most obvious complexity added by humans is the natural connection they make between a particular location on adjacent time steps, whereas technically, the only meaning to this is due to people believing it to be so. But beyond that, a human's ability to evaluate the nature of their opponents would (hopefully) allow them to easily crush an opponent which stood still, rather than standing idly by while it crushed them.