Baker, Saxe, and Tenebaum: "Bayesian Theory of Mind" (2011)

I was referred to this paper by one of the reviewers of my own paper on multi-agent statistics, since both seemed to be about reasoning about other people's beliefs. Their paper is concerned with inferring one other person's belief-desire state from observed behavior, not with reasoning of arbitrarily high order (like I know that you know that I know…). This means that there are some issues in general multi-agent statistics that they don't have to worry about.

At any rate, the set-up they consider is the following:

• The subject observes a little stylized scene comparable to a simple video game interface.
• This scene features a little cartoonish character (a circle with two eyes).
• Depending on where the character is standing, different parts of the scene will be blocked from view.
• The scene contains two parking lots in which food trucks can park.
• There are three different kinds of food truck that may or may not be present in the scene.
• In each condition, the subject sees the little character move around in a certain predetermined way.

After watching this scene, the subjects were then asked to provide assessments of the little character's beliefs and food preferences. For instance, if the character could initially see a truck with Korean food, but still walked up to check the other parking lot, this must be because the person was wondering whether a more preferred kind of food was available.

The character sees the Korean truck, yet walks up and checks what else is available.

In the model, these videos were discretized and treated as a hidden Markov model with the desires (food preference ordering) and beliefs (about which trucks there might be in the parking lots) as hidden states.

At each time step, previous actions inform new states of the world.

Since there were actually a quite small space of possible routes and possible plans, the model could in fact have been simplified immensely in this case, although at the expense of generalizability.