Figure 1.

Task and Agent Summary: In the Ultimatum Game, a sender (orange) chooses how much of an endowment to send to a receiver (blue). The receiver then has a chance to either accept or reject this offer. If the receiver accepts, they both get to keep their portion of the endowment. If the receiver rejects, neither gets anything. In our simulations, we included two types of sender and two types of receiver. The first type of sender has a Depth of Mentalization of –1 (DoM(–1)) – it possesses no Theory of Mind and is simply reactive to the receiver’s actions. In addition, we introduce a random sender, sending uniformly distributed offers. The other type of sender and both receivers are endowed with Theory of Mind along with DoM $\in \{0, 1, 2\}$. This enables these agents to model their partners recursively, to a strictly limited extent. Both agents are characterized by their DoM level and by a threshold, representing in principle the minimal reward they are willing to accept. Agents at DoM(>0) can conceptualise the world model of how others below them in the hierarchy perceive the self. Given the requirement of the IUG to balance short and long-term rewards, and given the types of agents available, this leads to strategic play by more sophisticated agents to get a greater frequency of more favourable outcomes. For example, a DoM(1) agent knows that the DoM(0) is able to conceptualise whether they are playing with a random or intentional sender, and therefore may behave in a way that causes the DoM(0) to mischaracterise the sender’s identity as random. This means the DoM(1) can then send very unfavourable offers knowing that the DoM(0) does not believe they can influence the outcome.