Attacking a Nuclear Facility with Noisy Intelligence and Signal Disruption

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Abstract: The paper analyses interaction between two enemy nations – Player 1 (the weak
nation) and Player 2 (the strong nation). 1 (he) wishes to develop a nuclear bomb and 2
(she) who employs an intelligence system, IS, aims to deter him by attacking 1. If 1 refuses
to open his facilities for inspection, 2’s IS will send a noisy signal indicating whether 1
builds a bomb (b) or not (nb). 1 has a disruptive technology (DT) which disrupts IS’s signal
with positive probability. Based on the signal sent by IS, 2 decides whether to attack 1
or not. The precision of IS is 2’s private information while the quality of DT is common
knowledge. The paper characterises the unique perfect Bayesian equilibrium of the game
and produces some surprising results. (1) Operating a better-quality DT lowers 1’s payoff,
therefore increases the probability 1 allows inspection and prevents a conflict. (2) Suppose
2 receives the signal b. If 1 estimates IS to be of high quality, 2 attacks 1 with probability
1. If, however, 1 estimates IS to be of low quality, 2 does not attack 1 with significant
probability. (3) As expected, a more precise IS benefits 2, and for some parameters even
benefits 1.

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