Alien species experience both costs and benefits in invaded environments, through naiveté of potential prey species, but also predation pressure from native predators. The question of whether alien prey recognise and respond to native predators has been relatively understudied, despite the hypothesised potential for native predators to provide biotic resistance to invasion. There are two main hypotheses about whether exotic prey should recognise native and exotic predators in their new ranges: (1) naiveté—predicting recognition of evolutionarily familiar predators only, and (2) pre-adaptation—predicting recognition of all predators through a generalist recognition template. With regards to antipredator responses, (3) naïveté theory presumes that exotic prey will respond to the predators they recognise, but we suggest that (4) a bold behavioural syndrome, and/or a high marginal value of food in invaded environments might result in weak or absent responses, even to recognised predators. Here we combine the giving-up density framework with behavioural analysis of remote camera footage to experimentally test these ideas in a disturbed, peri-urban, Australian ecosystem, where alien black rats are predated on by alien dogs, foxes, cats, and native quolls. Black rats recognised dogs and foxes, but appear naïve towards quolls. However, they showed no antipredator responses at all, consistent with a bold behavioural syndrome, elevated predation risk, and/or a high marginal value of food in invaded environments.