1. Game-Theoretic Approaches to Critical Infrastructure ProtectionWorkshop on Statistics and CounterterrorismNovember 20, 2004Vicki Bier University of Wisconsin-Madison

2. Research Objectives • Objective: • Study optimal allocation of resources for protection of systems against intentional attacks • Related to risk analysis: • With close tie to economics • (Game theory is a branch of economics) • Potentially applicable in many areas

3. Background • Because attackers can modify their strategies in response to our defensive investment: • Defense will generally be more costly when the adversary can observe the system defenses • “Investment in defensive measures, unlike investment in safety measures, saves a lower number of lives…than the apparent direct contribution of those measures” • Ravid (2002) • Security improvements may be less cost-effective than they would initially appear

4. Game Theory • Determine the optimal defense against an optimal attack • Game theory is a useful model for security and critical infrastructure protection: • Appropriate when protecting against intelligent and adaptable adversaries • Recognizes that defensive strategies must account for attacker behavior

5. Game between Attackers and Defenders • Need to make assumptions about: • Attacker goals and constraints • Defender goals and constraints • System design features • Protective investment assumed to reduce success probability of attacks

6. Game between Attackers and Defenders • Consider security of a simple series system: • Defending series systems against informed and determined attackers is a difficult challenge • If the attacker knows about the system’s defenses, the defender’s options are limited: • The defender is largely deprived of the ability to allocate defensive investments by their cost-effectiveness • Instead, defensive investments must equalize the “attractiveness” of all defended components

7. Importance of Redundancy • Parallel systems: • Any component can perform the function • Attacker must disable all to succeed • Series systems: • Attacker has a wide choice of targets • Defender must protect all components! • Physically in series (pipelines, electric lines) • Multiple failure modes (e.g., multiple points of entry)

8. Weakest Link Models • Defender must equalize the attractiveness of all defended components • This is generally consistent with the Brookings Institution recommendation to defend only the most valuable assets • However, terrorists also consider the probabilityof success in choice of targets: • So models should take the success probabilities of attacks against various targets into account

9. Attacker Knowledge • The assumption that attackers know our defenses may not be unrealistic: • Due to the openness of our society • Public demands knowledge of our defense: • Even when this weakens its effectiveness! • This increases difficulty of defense: • E.g., anthrax protection • Defensive measures may not be effective if they can be easily observed

10. System Design Features • Redundancy reduces attacker flexibility: • And increases defender flexibility • Traditional reliability design considerations: • Spatial separation • Functional diversity are also important to defensive strategy • Examples: • Defenses that do not require electricity • Use of both land lines and satellite communications • Secrecy and deception can also be valuable

11. Extensions with Hedging • Real-world decision makers will want to hedge: • In case they guess wrong about which targets are most attractive to attackers • Recent work assumes that attackers target the most attractive component: • But defenders are uncertain about their attractiveness • Attackers will in general have different values for targets than defenders: • For example, Al-Qaeda prefers targets that are “recognizable in the Middle East” (Woo)

12. Extensions with Hedging • Defending one target can deflect attacks to targets that are: • Less attractive to attackers (a priori) • But more damaging to defenders! • Optimal defense frequently still involves allocating zero resources to targets with a non-zero probability of successful attack, especially if: • Targets value widely in their values • Defender is highly resource-constrained

13. Sample Application • Our results shed light on appropriate allocation of resources among targets: • Focus on the most attractive (and most vulnerable) targets • Spend less money on targets that are unlikely to be attacked • Some states may have relatively few targets worth much investment 

14. Security versus Safety • In safety applications: • Natural hazards • Accident prevention the 80/20 rule works well: • Address the top 80% of the risks, at 20% of the cost • By contrast, in security applications: • It may not be worthwhile spending anything at all • Unless you address all serious vulnerabilities • Example: • Don’t bother searching purses and backpacks • If you don’t also search baby carriages!

15. Extensions in Progress • More complicated system structures: • E.g., adapting past work on least-cost diagnosis to identify “least-cost” attack strategies • As a building block for optimal (or near-optimal) defenses • Non-convex functions for attack success probability as a function of investment: • If minimal levels of investment are required • If investment beyond a threshold deters attackers • Secrecy and deception: • When are these useful? • How can we quantify their benefits?

16. Game between Defenders • Consider effects of defensive actions on the risks faced by other defenders: • And therefore the strategies they adopt • Some defenses (e.g., car alarms) increase risk to other defenders: • Payoff of investing to any one individual is greater than the net payoff to society • Typically leads to overinvestment in security • Other defenses (e.g., vaccination) decrease risk to other defenders: • “Free riders” • Typically lead to underinvestment in security

17. Game between Defenders • Extended an earlier “static” model by Kunreuther and Heal to account for attacks over time: • Example--computerized supply chain partners • Differences in discount rates can lead some agents not to invest in security when it is otherwise in their interests: • If other agents choose not to invest • Differences in discount rates can arise due to: • Industries with different rates of return • Risk of impending bankruptcy • Myopia • This game can have multiple equilibrium solutions: • Creating a need for coordinating mechanisms

18. Sample Application • Computer security in electronic supply chains: • Companies may be vulnerable to weaknesses in computer security on the part of their partners • This can reduce their incentives to invest in their own computer security • Coordinating mechanisms can help to address this problem: • Contract terms • Government regulation • Development of international standards • Loans to enable partners who are not as financially stable to improve their computer security

19. Conclusions • Protecting against intentional attacks must account for attacker responses: • Most applications of risk analysis fail to take this into account • Most applications of game theory to security deal with individual components in isolation • Combining these approaches makes it possible to invest more cost-effectively: • Avoids wasting resources on defenses that can easily be disabled or circumvented by attackers