The Three Prisoners Problem Revisited: issues in the use of Bayesian networks for security applications

Bayesian networks are a type of causal network used for probabilistic reasoning, which have found wide application in biomedical environments and machine vision.We have considered their application in the realm of security, where behaviour that is deliberately intended to deceive has to be considered. As a first step to the the analysis of this behaviour we have analysed problems in which an one agent provides truthfull, but evasive, information to the other agents. The three prisoners problem, and its simpler relation the Monty Hall problem, are classic examples of statistical analysis giving rise to counter intuitive results. In this paper the source of the counter intuitive results is identified as an agent that only releases partial data about the true state of the system. Furthermore the data that is communicated is a function of the identity of the agent requesting the data. Under these circumstances two significant results are demonstrated; first different questioning agents, will arrive at different probability estimates for the same problem. Secondly, although if all the data is requested the estimated probability will converge, the convergence may be nonmonotonic. This means that some questions, truthfully answered, will lead to a less precise probability measurement. Keywords — Bayesian reasoning; three prisoner problem;