Table 1.

Summary of DoM levels and behaviours. Here we refer to ‘self’ to mean the subject of the belief, and ‘other’ to mean the partner.

	DoM(–1)	DoM(0)	DoM(1)	DoM(2)
DoM characterisation	None	Infer direct action about the other irrespective of the self	Consider others’ beliefs about the self	Consider other’ beliefs about the self thinking about the other
Formalism	None	$b_{k=\mathrm{\text{0}}}(\theta )=P({\eta }_{k=–1})$	$b_{k=1}(\theta )=P\left({\eta }_{k=0}\right)\times b_{k=0}(\theta )$	$b_{k=2}(\theta )=P\left({\eta }_{k=1}\right)\times b_{k=1}(\theta )$
Strategic behaviour	Reactive	Identification of the other based on their history of actions	Belief manipulation based on an other’s model (k–1) of the self	Skepticism, Counter-deceptive knowledge that a DoM(1) agent will try and deceive
Task behaviour	Responds to action based on a fixed policy	Adapted behaviour to observations given the identified opponent type	Selects actions to manipulate beliefs given the known world model of a DoM(0) agent	Identify deceptive behaviour and counter-deceive DoM(1)
Vulnerability	DoM(0) manipulation	DoM(1) manipulation	DoM(2) counter-deceptive manipulation	Overmentalizing about DoM(0) and DoM(–1)