Jul 2026· International Game Theory Review· 1 citation
TL;DR
The Sonin’s complex ”fill-and-switch” strategy is reduced to a simple threshold rule: the attacker targets nodes with a negative signal when the sum of sensitivity and specificity is greater than one, and randomizes when the sum is one.
Abstract
This paper studies an attack-defense game with incomplete information. The game involves two players: the defender and the attacker. The defender locks objects. The attacker then tests the objects and obtains information with random errors. When attacking an unlocked object, the attacker wins the game. Sonin’s complex ”fill-and-switch” strategy is reduced to a simple threshold rule: the attacker targets nodes with a negative signal when the sum of sensitivity and specificity is greater than one, nodes with a positive signal when the sum is less than one, and randomizes when the sum is one. The defender allocates locks uniformly at random. Exact expressions for the attacker’s equilibrium strategy are obtained, as well as analytical expressions for the game value. The game value satisfies duality, reaches its minimum when the sum of sensitivity and specificity is one, and converges to the node value at rate [Formula: see text]. This makes the LBT model a practical tool for security applications.
It is demonstrated that under certain initial conditions, the Attackers can mislead the Defender into making suboptimal decisions through a slow-speed deception strategy, achieving superior payoffs compared to the complete information game.
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