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allocator. These results are compatible with earlier research into the advantage
of higher-order theory of mind in competitive settings [24, 25]. However, we did
not find any benefit for the use of third-order theory of mind here. A possible
explanation is that the settings in [24, 25] are zero-sum games, while allocators
in Colored Trails compete for the opportunity to trade with a responder. In
Colored Trails, an allocator of a higher order of theory of mind generally makes
an offer that is more beneficial to the responder at the expense of his own score.
We compared the performance of allocators that made offers based on iterated
best-response models with allocators that form utility proportional beliefs. Allo-
cators that form beliefs based on iterated best-response models believe that ev-
ery agent is a utility-maximizing agent, while an agent with utility-proportional
beliefs takes into account that competing allocators may make mistakes. Inter-
estingly, although our model did not include mistakes, iterated best-response
agents did not outperform agents with utility-proportional beliefs.
Our results suggest that in mixed teams of humans and agents, agents that
make use of theory of mind will perform better. Based on the experiments in
Colored Trails, we expect that cognitive agents will suffer diminishing returns
on higher orders of theory of mind. Interestingly, similar results are found for
human participants [5], who do well on first-order theory of mind tasks, and have
increasingly more diculty with higher-order theory of mind tasks. In future
work, we intend to compare the performance of human participants and theory
of mind agents by letting them play directly against each other.
In future research, we aim to increase the emphasis on the mixed-motive
nature of Colored Trails by allowing multiple rounds of negotiations. A responder
that is allowed to make offers would benefit from considering the beliefs of others.
This may give an allocator incentive to consider these beliefs of the responder in
his initial offer. Higher orders of theory of mind may also become more effective
when the game setting is not fully observable. In our setup, agents know the
initial location, the goal location, and the chips in possession of every player.
However, in everyday negotiation situations, the goals of the participants are
usually not fully known [26]. Higher orders of theory of mind may be beneficial
in determining the information available to each agent, as well as the information
that agents may be revealing or trying to hide by making a specific offer.
Acknowledgments.
This work was supported by the Netherlands Organisation
for Scientific Research (NWO) Vici grant NWO 277-80-001 awarded to Rineke
Verbrugge.
References
1. Premack, D., Woodruff, G.: Does the chimpanzee have a theory of mind? Behav.
Brain Sci. 1(04), 515-526 (1978)
2. Perner, J., Wimmer, H.: “John thinks that Mary thinks that...”. Attribution of
second-order beliefs by 5 to 10 year old children. J. Exp. Child Psychol. 39(3),
437-471 (1985)
