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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.


Ma, Siyu, Yair Tauman, and Richard Zeckhauser. "Deterrence games and the disruption of information." International Journal of Game Theory 53 (March 2024): 261-287.