The Importance of Another Person’s Hat

This week I am going to expand on the concept of looking from the view of the other players. To an infinite degree actually. But first let me go back to the beginning and to what you can do when viewing a game from another person’s shoes. The simplest form of this I already explained, which is the elimination of dominated strategies. To resummarize, it is finding what choices will always be worse than another no matter what others do, and removing them from the scenario.

However there is two assumption that was made to perform the elimination of the other player’s strategy. It’s a simple one as well, it was assumed that the other player had the same information as we did. Now while this is always a safe assumption, it can be dangerous down the line. For example if the other player did not know the payoffs, they would not have any reason to eliminate a dominated strategy. In that case, it would be smarter to assume it is equally probable that they choose any of the options, since deleting a dominated strategy might get rid of a possible better payoff.

This second assumption is that we are playing against another rational player who knows to look for dominated strategies. This is a much less safe assumption, since not every person thinks rationally or knows to look for things such as dominated strategies in a game. So this means it is important to not just know what another player knows, but how they are thinking. Two people, presented with the exact same options, will often make different choices. This is not because one is smarter than the other, but because they view the options differently. One might be trying to get the best singular outcome while the other is going for the best overall outcome. So remember this the next time you are trying to predict what someone is going to do. Think not only about what information they have in front of them, but how they will interpret it. This will get you closer to the best possible outcome for yourself.

This also leads into what I think is a fascinating concept, common knowledge. Common knowledge is the process of being able to say ‘I know you know I know I know…” infinitely about something. This is so important since this is vital to predict how other people will react to something. While this may seem quite simple it can have hiccups. Let me use the picture at the top that probably seemed out of place until now. Here is the scenario: there are two people who had hats placed on their heads, but each person does not know what color his hat is. However each person can see the color of the others hat. So here is the question, is the statement “there is at least one black hat” common knowledge. At first glance it may seem so, but in truth it is not common knowledge. The mental catch comes in the fact that each person knows there is a black hat in the room. However, they do not know if the other person is seeing a black hat as the color of their own hat is unknown to them. This is called mutual knowledge, where each person know something, but are unaware that the other players are know that same thing. Keep this in mind when putting yourself in someone else’s shoes, so as not to assume that the person always knows what you know

Thanks for reading, I hope you learned something.


For anyone who wants to follow their own interest in game theory, here are a few resources:

5 thoughts on “The Importance of Another Person’s Hat

  1. Max D.

    Hi Tom, I love the idea of using a simple game to explain more abstract concepts so that they seem more tangible. However, I think it would be better if you describe the Hat Puzzle is before you get into more details.

  2. Susan Waterhouse

    I like your comment about not knowing what others will do. In thinking about what others might do, there are always options that are purposely not optimizing a current turn for the player, but still might be “rational”. eg, a player trying a new strategy… what happens if I? Or playing to take opportunities from another player.

  3. margaretjhaviland

    Susan makes an interesting point about motives and reasons for choosing a not optimal option. What does Game Theory suggest we do in these situations to maximize our own outcomes even as we know our opponent may choose for unfathomable reasons?

  4. rickyyu1999

    This is a really cool train of thought/theory. I’m wondering if this has anything to do with the Game Theory in an Oligopoly market system taught during Macroeconomics. It sounds very similar as in people and organizations consider options that would hurt them less no matter what the other person chooses.


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