defensedominated

Defensedominated is a term used in decision analysis and security game theory to describe a defensive action, strategy, or position that is at least as effective as all other defensive options against every possible action by an adversary, and strictly more effective for at least one adversary action. It is related to the idea of a dominant strategy, but it is defined with respect to the defender’s payoffs across the set of possible attacker moves.

Formally, consider a defender choosing among defensive options D1, D2, ..., Dn and an attacker choosing among actions A1, A2, ..., Am. A defensive option Dk is defense-dominated if, for every attacker action Aj, the defender’s payoff when using Dk against Aj is greater than or equal to the payoff obtained by using any other defensive option Di against Aj, with strict inequality for at least one Aj. If such a Dk exists, it is a robust defense choice because it performs at least as well as alternatives under all attacker responses and better in at least one case.

Relation to dominated strategies: a defense option that is defense-dominated by another can be discarded from consideration, as it cannot yield a higher payoff than the dominating option in any scenario. The concept helps simplify strategic analysis in security games, risk management, and defensive planning.

Applications and limitations: defense-dominated reasoning is common in cybersecurity resource allocation, military protection, and risk mitigation where defender payoffs are well-specified. However, not all decision problems produce a defense-dominated option, especially in environments with high uncertainty or when attacker behavior is unpredictable. See also dominated strategy, dominant strategy, and robust optimization.