Agent-Based Models for Higher-Order Theory of Mind - Advances in Social Simulation - page 219

The focal allocator benefits from higher-order theory of mind when he com-
petes with an allocator that can reason about the mental states of others. Paired
t tests show that for any order of theory of mind of the competing allocator, per-
formance of a focal ToM 2 allocator differs significantly from the performance of a
focal ToM 1 allocator. However, this difference is low compared to the advantage
the focal ToM 1 allocator has over the focal ToM 0 allocator. Orders of theory of
mind higher than the second do not seem to benefit an allocator significantly. As
a result, the average score of the focal ToM 3 allocator is not consistently higher
than the average score of the focal ToM 2 allocator.
Figure 5 and Figure 6 summarize the performance of agents that differ in the
way they form beliefs about other agents. The distributions differ significantly
(K-S, p< 0 . 01), but one needs to look carefully to see the differences. For agents
that form beliefs based on iterated best-response, a ToM i allocator is correct
in his beliefs when the competing allocator is a ToM i− 1 agent. However, these
agents do not consider the possibility that their beliefs may be wrong. In Figure
5, this results in a stronger advantage for having correct beliefs. In particular,
when facing a competing ToM 0 allocator, the focal ToM 1 allocator performs
best, while the average score of the focal ToM 2 allocator is the highest when the
competing allocator is a ToM 1 agent.
Agents that form utility-proportional beliefs are never completely correct in
their beliefs, since their beliefs reflect the possibility of mistakes. Figure 6 shows
that as a result, the focal allocator has less of an advantage for being exactly one
order of theory of mind higher than the competing allocator. Interestingly, this
does not appear to cause lower performance of agents with utility-proportional
beliefs compared to agents with iterated best-response beliefs.
6 Discussion and Conclusion
Many of the interactions that people engage in on a daily basis involve mixed
motives, which are not fully competitive or fully cooperative. When the goals
of interacting individuals overlap, there may be an advantage to considering the
goals and beliefs of others explicitly, through a theory of mind. In this paper,
we investigated whether agents benefit from the ability to reason about higher
orders of theory of mind in the particular mixed-motive setting Colored Trails.
In the setting of Colored Trails we used, agents were put into the role of
either allocator or responder [14]. The agents engaged in single-shot negotiations,
where allocators made an offer which the responder could either reject or accept.
Allocator agents were found to benefit greatly from first-order theory of mind,
allowing them to consider the goals of other agents when making an offer.
Allocators could also benefit from higher-order theory of mind through com-
petition with another allocator. Our results showed that second-order theory of
mind benefits allocators whenever the competing allocator also has a theory of
mind. By recognizing that competitors may also consider the point of view of the
responder, second-order theory of mind allowed allocators to offer trades that
the responder accepted more often than the offers of a first-order theory of mind