Focal Points in Breath of the Wild

In my estimation, The Legend of Zelda: Breath of the Wild is the greatest video game of all time. There are a lot of reasons I think this is true. But, for now, I want to focus on the reason applicable to this website: game theory.

For the narrow set of readers familiar with both BotW and game theory, this might seem puzzling. Game theory is, by definition, the study of strategic interdependence. BotW is a one player game and would thus seem relegated to the field of decision theory.

On the contrary, a good portion of your play time is actually a two player game. It’s you and the game developer, and it’s a cooperative interaction.

Introducing the Game
BotW gives you the premise of the game-within-the-game right off the bat. As Link departs the Shrine of Resurrection, the camera guides you down a clear path. The first stop is a chat with the mysterious man at the campfire. Immediately afterward, Link finds a pointed ledge overlooking a pond.


Without telling you, the game is communicating a clear message. It is giving you a diving board shaped rock, equipped with its own water lily target. The game begs you to jump in. It then rewards Link with his first Korok seed.

Mr. Korok then tells you how the rest of this subquest will play out. Other Koroks are hidden, and you need to find them.

From here, the developers could have gone in two directions. One would have been a disaster. The other would make the game fun. They chose the latter.

Focal Points and Thomas Schelling
To get the fun, we must first take a step back and learn about focal points. In Strategy of Conflict, Thomas Schelling proposes the following problem. Suppose I instantly transport you and a friend to New York City. You have no way to communicate with each other but need to reunite. Where do you go to meet, and when do you do it?

This question has no “correct” answer. Anything you say—no matter how clever or ridiculous—could be right, as long as as your friend would say the same thing. Yet despite the infinite number of possibilities, Schelling found that people had a predisposition to choose Grand Central Station at noon.

Why? Schelling describes such a time and place as a “focal point.” They stand out for one reason or another, which makes them easier to coordinate on. Noon is the middle of the day, so it is a sensible time to meet someone else. Grand Central is a crossroads of New York, so it also seems appropriate.

The Developer’s Strategy
Nintendo could have placed the Koroks in the most obscure of places and make it as hard as humanly possible to find all of them. But they didn’t. Instead, they made a good faith effort to play a focal point coordination game with the player.

Open up your map and find another pool of water nearby? If you head there, a Korok is probably waiting for you. Is one tree much, much taller than the others? You should probably climb it. See a strange rock pattern in the distance? Time to investigate.

In fact, once you discover that category of Koroks, you look at your map in a whole new light:

Tons of these perfectly circular dots of rocks are all over the map. It makes you want to scour the map for more, and it excites you when you inadvertently discover one while using the map for something else.

Once you realize the game developers are trying to the Koroks easy to find, it completely changes your mindset. You start asking yourself “if I were a game developer who wanted to ‘hide’ Koroks in obvious places, where would I put them?”

Granted, not every Korok ends up feeling that way. The game has 900 of them, and the focal point is in the eye of the beholder. Many times, I was left dumbstruck and asking myself how anyone thought that someone could reasonably find that particular seed. Still, most of BotW rewards a type of strategic thinking that you rarely see in a one player game.


Adverse Selection and Cheap Talk in Pokémon: Let’s Go

Suppose you are a pokémon trainer, and a fellow trainer approaches you with the following proposition:

In any real life scenario, this should be a hard pass. But the situation provides a teachable moment on two fronts to justify that claim.

Adverse Selection
Suppose someone tells you they want to engage in a trade. What does that willingness tell you about whether you should do it?

In many contexts, it tells you a lot. Imagine the Exeggutor was the strongest one could possibly imagine. Would the person want to exchange it for another Exeggutor? Absolutely not—no matter the strength of the other Exeggutor the person could receive in return, it would be worse than what he currently has. So a strongest possible Exeggutor would never be offered up in a trade.

Iterating this logic has an interesting implication. Consider the incentives of someone who has the second-strongest possible Exeggutor. Would that person want to exchange it? The only way this could be worth the time is if the other trainer has the strongest possible Exeggutor. But we just discovered that another trainer would not offer such an Exeggutor. So the person with the second-strongest should have no interest in trading either.

What about the third? Well, the only way this would be good is if a strongest or second-strongest Exeggutor were available. But they won’t be. So someone who owns the third-strongest should not engage in a trade either.

That logic unravels all the way down. Even a trainer with a very, very weak Exeggutor should have no interest in a trade. Although it is true that the average Exeggutor is much stronger than the one the trainer currently has, the average Exeggutor being offered for trade is not. In fact, trainers would only want to engage in a trade if the Exeggutor is the worst possible.

This result is well-known in game theory as a product of adverse selection—a situation where one party has private information about the value of a transaction. More specifically, it is an application of the market for lemons, which uses the same mechanism to explain why it is so difficult to buy a quality used car.

Cheap Talk
“But wait!” one might say. “The fellow trainer has assured me that he is very proud of his Exeggutor. It must be not so bad after all.”

Not quite. This is classic cheap talk. The message the other trainer is communicating could just as easily be conveyed by a trainer who actually thinks that his Exeggutor is terrible. Moreover, he does not have a common interest with you in communicating truthful information. Combining these pieces of information together, you should ignore the message altogether.

To make this more concrete, imagine that you were to take whatever the trainer said at his word. Then would a trainer with a truly terrible Exeggutor want to lie? If doing so would convince you to make the trade, then the answer is yes. As a result, you cannot differentiate between an honest assessment and a fib. In turn, the message should not change your beliefs about the Exeggutor’s quality at all.

Nintendo and Strategic Theory
All that said, this is Nintendo we are talking about. They are not interested in teaching you interdependent strategic thinking. The man actually has an exotic Exeggutor from a region you cannot access in the game. The only way to acquire such an Exeggutor is through a trade. You therefore most definitely should make the deal with him.

But this leads to a deeper question: why doesn’t the trainer just lead with that point in the first place? Rather than speaking to your common interest—he has an Exeggutor from his region and wants one from your region, you have an Exeggutor from your region and want one from his—he just speaks strategic nonsense.

Here’s hoping that George Akerlof appears in Pokemon: Sword and Shield offering the same trade. But this time, when you accept, you get a level 1 Exeggutor with all the minimum stats.