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. 2024 Sep 11;8(1):159–177. doi: 10.5334/cpsy.117

Figure 4.

Counter deceptive policy of high theory of mind agents

Dynamics of the DoM(2) counter-manipulation: (A) The DoM(2) with low threshold, masquerading as the high threshold receiver, rejects low offers. This encourages the DoM(1) sender with a high threshold to improve its offers, while having little effect on the already “generous” η = 0.1 DoM(1) sender. (B), the DoM(2) receiver correctly reads the DoM(1) sender’s strategy, while manipulating the latter’s beliefs (D) As depicted in (D), this causes the DoM(1) to develop false beliefs about the identity of the DoM(2) as they are unable to model them appropriately. (C) Typically, the agent with the higher DoM gains a higher reward than the lower DoM agent. The y-axis measures the ratio between the receiver and sender’s total reward. Due to the asymmetric nature of the IUG, the DoM(2) receiver superiority is manifested in its ability to lower the DoM(1) sender advantage.

Note: Posterior P. means the posterior distribution of the inferring agent after observing the actions of the other agent. P = 0 means that the inferring agent’s belief places zero probability that the observed agent has type θ and P = 1 means that the inferring agent is certain that the observed agent has type θ (when lines overlap the behaviour of the DoM(1) sender are the same for both thresholds).