When detecting a predator, some prey animals respond in a counterintuitive fashion by approaching, rather than fleeing, that potential threat of extinction. This seemingly paradoxical behaviour, known as predator inspection, has been reported for a wide variety of taxa-and therefore can be assumed to be adaptive. However, the view of predator inspection as a paradoxical behaviour rests on two implicit assumptions: (a) initial predator detecting is unambiguous, with no uncertainty in discriminating between hunting and non hunting members of predator species, or members of predator species and unrelated phenomena; (b) the costs of flight are negligible relative to the risk of predation. Upon reflection assumption (a) is not really tenable. Whereas assumption (b) is not consistent with experimental evidence [Godin & Crossman (1994) Behav. Ecol. Sociobiol.34, 359-366]. Given that predator detection is ambiguous and the costs of flight are not negligible, a prey individual may benefit by a closer approach to the source of the alarming signals, thus improving its assessment of the situation-despite the increased risk of predation. In this paper, the above statement is given rigor by reformulating the problem in game theoretical terms. The results indicate that a prey will minimize its costs by performing predator inspection whenever its degree of certainty regarding predator identification and/or assessment of its intentions is less than a threshold, which is determined by the model's parameters. Copyright 1999 Academic Press.