Protecting complex infrastructures against multiple strategic attackers

Infrastructures are analysed subject to defence by a strategic defender and attack by multiple strategic attackers. A framework is developed where each agent determines how much to invest in defending versus attacking each of multiple targets. A target can have economic, human and symbolic values, which generally vary across agents. Investment expenditure functions for each agent can be linear in the investment effort, concave, convex, logistic, can increase incrementally, or can be subject to budget constraints. Contest success functions (e.g., ratio and difference forms) determine the probability of a successful attack on each target, dependent on the relative investments of the defender and attackers on each target, and on characteristics of the contest. Targets can be in parallel, in series, interlinked, interdependent or independent. The defender minimises the expected damage plus the defence expenditures. Each attacker maximises the expected damage minus the attack expenditures. The number of free choice variables equals the number of agents times the number of targets, or lower if there are budget constraints. Each agent is interested in how his investments vary across the targets, and the impact on his utilities. Alternative optimisation programmes are discussed, together with repeated games, dynamic games and incomplete information. An example is provided for illustration.