Deterrence games and the disruption of information

Deterrence is a generic situation where a “Retaliator” (Player R) threatens to bash an “Underminer” (Player U) should he take a stealth threatening move. A typical Underminer is a potential bomb builder, market invader or computer hacker. The Retaliator’s decision whether to bash will depend on a noisy signal her intelligence receives about U’s action. U may or may not have the ability to disrupt R’s signal (type U⁺ and U^-, respectively). U’s type is his private information. If U can and does disrupt, the signal to R’s intelligence is random, in effect noise. The equilibrium of the game is basically unique. U is better off with the disruption capability than without. More accurate intelligence makes R less likely to bash U. Accordingly, all expected payoffs increase. As R’s belief about U’s ability to disrupt increases, R is more aggressive and U (whether he is able to disrupt or not) is less aggressive. Yet, greater disruption potentially lowers the payoffs of the all players R, U⁺ and U^-. Hence a more transparent information system with no potential disruption helps both sides.