Socially smart software agents entice people to use higher-order theory of mind in the Mod game

In social settings, people often need to reason about unobservable
mental content of other people, such as their beliefs, goals, or
intentions. This ability helps them to understand, to predict, and even
to influence the behavior of others. People can take this ability further
by applying it recursively. For example, they use second-order theory of
mind to reason about the way others use theory of mind, as in ‘Alice
believes that Bob does not know about the surprise party’. However,
empirical evidence so far suggests that people do not spontaneously use
higher-order theory of mind in strategic games. Previous agent-based
modeling simulations also suggest that the ability to recursively apply
theory of mind may be especially effective in competitive settings. In
this paper, we use a combination of computational agents and Bayesian
model selection to determine to what extent people make use of higherorder
theory of mind reasoning in a particular competitive game, the
Mod game, which can be seen as a much larger variant of the well-known
rock-paper-scissors game.
We let participants play the competitive Mod game against computational
theory of mind agents. We find that people adapt their level of
theory of mind to that of their software opponent. Surprisingly, knowingly
playing against second- and third-order theory of mind agents entices
human participants to apply up to fourth-order theory of mind
themselves, thereby improving their results in the Mod game. This phenomenon
contrasts with earlier experiments about other strategic oneshot
and sequential games, in which human players only displayed lower
orders of theory of mind.